Feigin–Frenkel center in types B, C and D View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-03-02

AUTHORS

A. I. Molev

ABSTRACT

For each simple Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{g}$\end{document} consider the corresponding affine vertex algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$V_{\mathrm{crit}}(\mathfrak{g})$\end{document} at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev’s discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of the centers of the affine vertex algebras \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$V_{\mathrm {crit}}(\mathfrak{g})$\end{document} associated with the simple Lie algebras \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{g}$\end{document} of types B, C and D. The construction relies on the Schur–Weyl duality involving the Brauer algebra, and the generators are expressed as weighted traces over tensor spaces and, equivalently, as traces over the spaces of singular vectors for the action of the Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{sl}_{2}$\end{document} in the context of Howe duality. This leads to explicit constructions of commutative subalgebras of the universal enveloping algebras \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{U}(\mathfrak{g}[t])$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{U}(\mathfrak{g})$\end{document}, and to higher order Hamiltonians in the Gaudin model associated with each Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{g}$\end{document}. We also introduce analogues of the Bethe subalgebras of the Yangians \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Y}(\mathfrak{g})$\end{document} and show that their graded images coincide with the respective commutative subalgebras of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{U}(\mathfrak{g}[t])$\end{document}. More... »

PAGES

1-34

References to SciGraph publications

  • 1996-05. Bethe subalgebras in twisted Yangians in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1988-02. Sugawara operators and Kac-Kazhdan conjecture in INVENTIONES MATHEMATICAE
  • 2006-04-02. Finite vs affine W-algebras in JAPANESE JOURNAL OF MATHEMATICS
  • 2006-07. The argument shift method and the Gaudin model in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 1994-12. Gaudin model, Bethe Ansatz and critical level in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2006-11-24. On the R-Matrix Realization of Yangians and their Representations in ANNALES HENRI POINCARÉ
  • 2006-01. The quantum Gaudin system in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 1971-08. Projection operators for simple lie groups in THEORETICAL AND MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00222-012-0390-7

    DOI

    http://dx.doi.org/10.1007/s00222-012-0390-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1048286925


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "School of Mathematics and Statistics, University of Sydney, 2006, Sydney, NSW, Australia", 
              "id": "http://www.grid.ac/institutes/grid.1013.3", 
              "name": [
                "School of Mathematics and Statistics, University of Sydney, 2006, Sydney, NSW, Australia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Molev", 
            "givenName": "A. I.", 
            "id": "sg:person.010630122575.07", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010630122575.07"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf02099459", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034039744", 
              "https://doi.org/10.1007/bf02099459"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10688-006-0030-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048211328", 
              "https://doi.org/10.1007/s10688-006-0030-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00023-006-0281-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039436899", 
              "https://doi.org/10.1007/s00023-006-0281-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10688-006-0012-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008127137", 
              "https://doi.org/10.1007/s10688-006-0012-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02099300", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032000985", 
              "https://doi.org/10.1007/bf02099300"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01038003", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007997906", 
              "https://doi.org/10.1007/bf01038003"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11537-006-0505-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041537938", 
              "https://doi.org/10.1007/s11537-006-0505-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01394343", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036489288", 
              "https://doi.org/10.1007/bf01394343"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2012-03-02", 
        "datePublishedReg": "2012-03-02", 
        "description": "For each simple Lie algebra \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathfrak{g}$\\end{document} consider the corresponding affine vertex algebra \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$V_{\\mathrm{crit}}(\\mathfrak{g})$\\end{document} at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev\u2019s discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of the centers of the affine vertex algebras \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$V_{\\mathrm {crit}}(\\mathfrak{g})$\\end{document} associated with the simple Lie algebras \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathfrak{g}$\\end{document} of types B, C and\u00a0D. The construction relies on the Schur\u2013Weyl duality involving the Brauer algebra, and the generators are expressed as weighted traces over tensor spaces and, equivalently, as traces over the spaces of singular vectors for the action of the Lie algebra \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathfrak{sl}_{2}$\\end{document} in the context of Howe duality. This leads to explicit constructions of commutative subalgebras of the universal enveloping algebras \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathrm{U}(\\mathfrak{g}[t])$\\end{document} and \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathrm{U}(\\mathfrak{g})$\\end{document}, and to higher order Hamiltonians in the Gaudin model associated with each Lie algebra \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathfrak{g}$\\end{document}. We also introduce analogues of the Bethe subalgebras of the Yangians \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathrm{Y}(\\mathfrak{g})$\\end{document} and show that their graded images coincide with the respective commutative subalgebras of\u00a0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$\\mathrm{U}(\\mathfrak{g}[t])$\\end{document}.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s00222-012-0390-7", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136369", 
            "issn": [
              "0020-9910", 
              "1432-1297"
            ], 
            "name": "Inventiones Mathematicae", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "191"
          }
        ], 
        "keywords": [
          "simple Lie algebras", 
          "affine vertex algebra", 
          "Lie algebra", 
          "vertex algebras", 
          "commutative subalgebra", 
          "commutative associative algebra", 
          "universal enveloping algebra", 
          "Schur\u2013Weyl duality", 
          "higher-order Hamiltonians", 
          "Gaudin model", 
          "Gaudin Hamiltonians", 
          "associative algebra", 
          "enveloping algebra", 
          "Brauer algebra", 
          "remarkable theorem", 
          "algebra", 
          "Howe duality", 
          "singular vectors", 
          "explicit formula", 
          "subalgebra", 
          "explicit construction", 
          "tensor space", 
          "order Hamiltonian", 
          "Bethe subalgebras", 
          "simple formula", 
          "Hamiltonian", 
          "duality", 
          "Yangian", 
          "formula", 
          "space", 
          "Feigin", 
          "theorem", 
          "generator", 
          "Frenkel", 
          "images coincide", 
          "coincide", 
          "construction", 
          "vector", 
          "model", 
          "critical level", 
          "traces", 
          "structure", 
          "center", 
          "analogues", 
          "types", 
          "discovery", 
          "context", 
          "decades", 
          "action", 
          "type B", 
          "levels"
        ], 
        "name": "Feigin\u2013Frenkel center in types B, C and D", 
        "pagination": "1-34", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1048286925"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00222-012-0390-7"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00222-012-0390-7", 
          "https://app.dimensions.ai/details/publication/pub.1048286925"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-12-01T06:29", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20221201/entities/gbq_results/article/article_559.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s00222-012-0390-7"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00222-012-0390-7'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00222-012-0390-7'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00222-012-0390-7'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00222-012-0390-7'


     

    This table displays all metadata directly associated to this object as RDF triples.

    140 TRIPLES      21 PREDICATES      83 URIs      67 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00222-012-0390-7 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N9984cd32b0084ceea9995df7c96e7d09
    4 schema:citation sg:pub.10.1007/bf01038003
    5 sg:pub.10.1007/bf01394343
    6 sg:pub.10.1007/bf02099300
    7 sg:pub.10.1007/bf02099459
    8 sg:pub.10.1007/s00023-006-0281-9
    9 sg:pub.10.1007/s10688-006-0012-5
    10 sg:pub.10.1007/s10688-006-0030-3
    11 sg:pub.10.1007/s11537-006-0505-2
    12 schema:datePublished 2012-03-02
    13 schema:datePublishedReg 2012-03-02
    14 schema:description For each simple Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{g}$\end{document} consider the corresponding affine vertex algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$V_{\mathrm{crit}}(\mathfrak{g})$\end{document} at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev’s discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of the centers of the affine vertex algebras \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$V_{\mathrm {crit}}(\mathfrak{g})$\end{document} associated with the simple Lie algebras \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{g}$\end{document} of types B, C and D. The construction relies on the Schur–Weyl duality involving the Brauer algebra, and the generators are expressed as weighted traces over tensor spaces and, equivalently, as traces over the spaces of singular vectors for the action of the Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{sl}_{2}$\end{document} in the context of Howe duality. This leads to explicit constructions of commutative subalgebras of the universal enveloping algebras \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{U}(\mathfrak{g}[t])$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{U}(\mathfrak{g})$\end{document}, and to higher order Hamiltonians in the Gaudin model associated with each Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{g}$\end{document}. We also introduce analogues of the Bethe subalgebras of the Yangians \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Y}(\mathfrak{g})$\end{document} and show that their graded images coincide with the respective commutative subalgebras of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{U}(\mathfrak{g}[t])$\end{document}.
    15 schema:genre article
    16 schema:isAccessibleForFree true
    17 schema:isPartOf N241a9d9a51f442ea9e07185281f90fdd
    18 N590a3a57aba548a5b2d9e6455ab6ef20
    19 sg:journal.1136369
    20 schema:keywords Bethe subalgebras
    21 Brauer algebra
    22 Feigin
    23 Frenkel
    24 Gaudin Hamiltonians
    25 Gaudin model
    26 Hamiltonian
    27 Howe duality
    28 Lie algebra
    29 Schur–Weyl duality
    30 Yangian
    31 action
    32 affine vertex algebra
    33 algebra
    34 analogues
    35 associative algebra
    36 center
    37 coincide
    38 commutative associative algebra
    39 commutative subalgebra
    40 construction
    41 context
    42 critical level
    43 decades
    44 discovery
    45 duality
    46 enveloping algebra
    47 explicit construction
    48 explicit formula
    49 formula
    50 generator
    51 higher-order Hamiltonians
    52 images coincide
    53 levels
    54 model
    55 order Hamiltonian
    56 remarkable theorem
    57 simple Lie algebras
    58 simple formula
    59 singular vectors
    60 space
    61 structure
    62 subalgebra
    63 tensor space
    64 theorem
    65 traces
    66 type B
    67 types
    68 universal enveloping algebra
    69 vector
    70 vertex algebras
    71 schema:name Feigin–Frenkel center in types B, C and D
    72 schema:pagination 1-34
    73 schema:productId N6a1770cce1c44f1c8349322edbd77804
    74 Nd706e22f2b9b4fd1aa4767469498a7f8
    75 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048286925
    76 https://doi.org/10.1007/s00222-012-0390-7
    77 schema:sdDatePublished 2022-12-01T06:29
    78 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    79 schema:sdPublisher N28609ed22c434ddd8f6524150e58b729
    80 schema:url https://doi.org/10.1007/s00222-012-0390-7
    81 sgo:license sg:explorer/license/
    82 sgo:sdDataset articles
    83 rdf:type schema:ScholarlyArticle
    84 N241a9d9a51f442ea9e07185281f90fdd schema:issueNumber 1
    85 rdf:type schema:PublicationIssue
    86 N28609ed22c434ddd8f6524150e58b729 schema:name Springer Nature - SN SciGraph project
    87 rdf:type schema:Organization
    88 N590a3a57aba548a5b2d9e6455ab6ef20 schema:volumeNumber 191
    89 rdf:type schema:PublicationVolume
    90 N6a1770cce1c44f1c8349322edbd77804 schema:name dimensions_id
    91 schema:value pub.1048286925
    92 rdf:type schema:PropertyValue
    93 N9984cd32b0084ceea9995df7c96e7d09 rdf:first sg:person.010630122575.07
    94 rdf:rest rdf:nil
    95 Nd706e22f2b9b4fd1aa4767469498a7f8 schema:name doi
    96 schema:value 10.1007/s00222-012-0390-7
    97 rdf:type schema:PropertyValue
    98 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    99 schema:name Mathematical Sciences
    100 rdf:type schema:DefinedTerm
    101 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    102 schema:name Pure Mathematics
    103 rdf:type schema:DefinedTerm
    104 sg:journal.1136369 schema:issn 0020-9910
    105 1432-1297
    106 schema:name Inventiones Mathematicae
    107 schema:publisher Springer Nature
    108 rdf:type schema:Periodical
    109 sg:person.010630122575.07 schema:affiliation grid-institutes:grid.1013.3
    110 schema:familyName Molev
    111 schema:givenName A. I.
    112 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010630122575.07
    113 rdf:type schema:Person
    114 sg:pub.10.1007/bf01038003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007997906
    115 https://doi.org/10.1007/bf01038003
    116 rdf:type schema:CreativeWork
    117 sg:pub.10.1007/bf01394343 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036489288
    118 https://doi.org/10.1007/bf01394343
    119 rdf:type schema:CreativeWork
    120 sg:pub.10.1007/bf02099300 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032000985
    121 https://doi.org/10.1007/bf02099300
    122 rdf:type schema:CreativeWork
    123 sg:pub.10.1007/bf02099459 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034039744
    124 https://doi.org/10.1007/bf02099459
    125 rdf:type schema:CreativeWork
    126 sg:pub.10.1007/s00023-006-0281-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039436899
    127 https://doi.org/10.1007/s00023-006-0281-9
    128 rdf:type schema:CreativeWork
    129 sg:pub.10.1007/s10688-006-0012-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008127137
    130 https://doi.org/10.1007/s10688-006-0012-5
    131 rdf:type schema:CreativeWork
    132 sg:pub.10.1007/s10688-006-0030-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048211328
    133 https://doi.org/10.1007/s10688-006-0030-3
    134 rdf:type schema:CreativeWork
    135 sg:pub.10.1007/s11537-006-0505-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041537938
    136 https://doi.org/10.1007/s11537-006-0505-2
    137 rdf:type schema:CreativeWork
    138 grid-institutes:grid.1013.3 schema:alternateName School of Mathematics and Statistics, University of Sydney, 2006, Sydney, NSW, Australia
    139 schema:name School of Mathematics and Statistics, University of Sydney, 2006, Sydney, NSW, Australia
    140 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...