The quantum general linear supergroup, canonical bases and Kazhdan-Lusztig polynomials View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2009-03

AUTHORS

HeChun Zhang

ABSTRACT

Canonical bases of the tensor powers of the natural -module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several directions. We first construct the canonical bases of the ℤ2-graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra Oq(Mm|n) of a quantum (m,n) × (m,n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for by applying a quantum analogue of the Borel-Weil construction. More... »

PAGES

401-416

References to SciGraph publications

  • 1998-08. Structure and Representations of the Quantum General Linear Supergroup in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1998-12. Kazhdan-Lusztig polynomials and canonical basis in TRANSFORMATION GROUPS
  • 1991-11. UniversalR-matrix for quantized (super)algebras in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1979-06. Representations of Coxeter groups and Hecke algebras in INVENTIONES MATHEMATICAE
  • 1983. Left cells in weyl groups in LIE GROUP REPRESENTATIONS I
  • 2005-09. Dual Canonical Bases for the Quantum Special Linear Group and Invariant Subalgebras in LETTERS IN MATHEMATICAL PHYSICS
  • Journal

    TITLE

    Science in China Series A Mathematics

    ISSUE

    3

    VOLUME

    52

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11425-008-0150-8

    DOI

    http://dx.doi.org/10.1007/s11425-008-0150-8

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1033238182


    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/2008/0206", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Quantum Physics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/02", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Tsinghua University", 
              "id": "https://www.grid.ac/institutes/grid.12527.33", 
              "name": [
                "Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Zhang", 
            "givenName": "HeChun", 
            "id": "sg:person.07746267221.46", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07746267221.46"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1090/s0894-0347-00-00321-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011296100"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02102819", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012241757", 
              "https://doi.org/10.1007/bf02102819"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02102819", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012241757", 
              "https://doi.org/10.1007/bf02102819"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0071433", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013827773", 
              "https://doi.org/10.1007/bfb0071433"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11005-005-0015-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017319529", 
              "https://doi.org/10.1007/s11005-005-0015-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11005-005-0015-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017319529", 
              "https://doi.org/10.1007/s11005-005-0015-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0894-0347-1990-1035415-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027548652"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jalgebra.2005.11.023", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029386323"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01390031", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029855172", 
              "https://doi.org/10.1007/bf01390031"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0021-8693(91)90225-w", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031125256"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jalgebra.2006.01.053", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040687874"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200050401", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047558769", 
              "https://doi.org/10.1007/s002200050401"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01234531", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050464897", 
              "https://doi.org/10.1007/bf01234531"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01234531", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050464897", 
              "https://doi.org/10.1007/bf01234531"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.530198", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058107189"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/s0012-7094-91-06321-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064419691"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/s0012-7094-93-06920-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064419839"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2009-03", 
        "datePublishedReg": "2009-03-01", 
        "description": "Canonical bases of the tensor powers of the natural -module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several directions. We first construct the canonical bases of the \u21242-graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra Oq(Mm|n) of a quantum (m,n) \u00d7 (m,n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for by applying a quantum analogue of the Borel-Weil construction.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s11425-008-0150-8", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1312250", 
            "issn": [
              "1006-9283", 
              "1862-2763"
            ], 
            "name": "Science in China Series A Mathematics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "52"
          }
        ], 
        "name": "The quantum general linear supergroup, canonical bases and Kazhdan-Lusztig polynomials", 
        "pagination": "401-416", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "9e57444acc338bca6bc946b35b10b1e3a118730185b9e6f54b5fc33bdcd9869d"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s11425-008-0150-8"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1033238182"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s11425-008-0150-8", 
          "https://app.dimensions.ai/details/publication/pub.1033238182"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T09:10", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000338_0000000338/records_47968_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs11425-008-0150-8"
      }
    ]
     

    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/s11425-008-0150-8'

    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/s11425-008-0150-8'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11425-008-0150-8'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11425-008-0150-8'


     

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

    109 TRIPLES      21 PREDICATES      41 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s11425-008-0150-8 schema:about anzsrc-for:02
    2 anzsrc-for:0206
    3 schema:author N58fc9c37997b490f92e2024a4212530f
    4 schema:citation sg:pub.10.1007/bf01234531
    5 sg:pub.10.1007/bf01390031
    6 sg:pub.10.1007/bf02102819
    7 sg:pub.10.1007/bfb0071433
    8 sg:pub.10.1007/s002200050401
    9 sg:pub.10.1007/s11005-005-0015-9
    10 https://doi.org/10.1016/0021-8693(91)90225-w
    11 https://doi.org/10.1016/j.jalgebra.2005.11.023
    12 https://doi.org/10.1016/j.jalgebra.2006.01.053
    13 https://doi.org/10.1063/1.530198
    14 https://doi.org/10.1090/s0894-0347-00-00321-0
    15 https://doi.org/10.1090/s0894-0347-1990-1035415-6
    16 https://doi.org/10.1215/s0012-7094-91-06321-0
    17 https://doi.org/10.1215/s0012-7094-93-06920-7
    18 schema:datePublished 2009-03
    19 schema:datePublishedReg 2009-03-01
    20 schema:description Canonical bases of the tensor powers of the natural -module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several directions. We first construct the canonical bases of the ℤ2-graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra Oq(Mm|n) of a quantum (m,n) × (m,n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for by applying a quantum analogue of the Borel-Weil construction.
    21 schema:genre research_article
    22 schema:inLanguage en
    23 schema:isAccessibleForFree false
    24 schema:isPartOf N63e93a171c5c48a98058414b8a09a5f4
    25 N933aebc465d345ccbcab75eace87c109
    26 sg:journal.1312250
    27 schema:name The quantum general linear supergroup, canonical bases and Kazhdan-Lusztig polynomials
    28 schema:pagination 401-416
    29 schema:productId N37ddf628cdb845db9d5b021592d52a26
    30 N6890c1a6ba24408982d840a61eb7ecb0
    31 Nb0e8421723684000b42ad6d1e7c0218a
    32 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033238182
    33 https://doi.org/10.1007/s11425-008-0150-8
    34 schema:sdDatePublished 2019-04-11T09:10
    35 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    36 schema:sdPublisher N043feedcaece42788dce44b0d08cb32a
    37 schema:url http://link.springer.com/10.1007%2Fs11425-008-0150-8
    38 sgo:license sg:explorer/license/
    39 sgo:sdDataset articles
    40 rdf:type schema:ScholarlyArticle
    41 N043feedcaece42788dce44b0d08cb32a schema:name Springer Nature - SN SciGraph project
    42 rdf:type schema:Organization
    43 N37ddf628cdb845db9d5b021592d52a26 schema:name doi
    44 schema:value 10.1007/s11425-008-0150-8
    45 rdf:type schema:PropertyValue
    46 N58fc9c37997b490f92e2024a4212530f rdf:first sg:person.07746267221.46
    47 rdf:rest rdf:nil
    48 N63e93a171c5c48a98058414b8a09a5f4 schema:issueNumber 3
    49 rdf:type schema:PublicationIssue
    50 N6890c1a6ba24408982d840a61eb7ecb0 schema:name dimensions_id
    51 schema:value pub.1033238182
    52 rdf:type schema:PropertyValue
    53 N933aebc465d345ccbcab75eace87c109 schema:volumeNumber 52
    54 rdf:type schema:PublicationVolume
    55 Nb0e8421723684000b42ad6d1e7c0218a schema:name readcube_id
    56 schema:value 9e57444acc338bca6bc946b35b10b1e3a118730185b9e6f54b5fc33bdcd9869d
    57 rdf:type schema:PropertyValue
    58 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
    59 schema:name Physical Sciences
    60 rdf:type schema:DefinedTerm
    61 anzsrc-for:0206 schema:inDefinedTermSet anzsrc-for:
    62 schema:name Quantum Physics
    63 rdf:type schema:DefinedTerm
    64 sg:journal.1312250 schema:issn 1006-9283
    65 1862-2763
    66 schema:name Science in China Series A Mathematics
    67 rdf:type schema:Periodical
    68 sg:person.07746267221.46 schema:affiliation https://www.grid.ac/institutes/grid.12527.33
    69 schema:familyName Zhang
    70 schema:givenName HeChun
    71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07746267221.46
    72 rdf:type schema:Person
    73 sg:pub.10.1007/bf01234531 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050464897
    74 https://doi.org/10.1007/bf01234531
    75 rdf:type schema:CreativeWork
    76 sg:pub.10.1007/bf01390031 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029855172
    77 https://doi.org/10.1007/bf01390031
    78 rdf:type schema:CreativeWork
    79 sg:pub.10.1007/bf02102819 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012241757
    80 https://doi.org/10.1007/bf02102819
    81 rdf:type schema:CreativeWork
    82 sg:pub.10.1007/bfb0071433 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013827773
    83 https://doi.org/10.1007/bfb0071433
    84 rdf:type schema:CreativeWork
    85 sg:pub.10.1007/s002200050401 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047558769
    86 https://doi.org/10.1007/s002200050401
    87 rdf:type schema:CreativeWork
    88 sg:pub.10.1007/s11005-005-0015-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017319529
    89 https://doi.org/10.1007/s11005-005-0015-9
    90 rdf:type schema:CreativeWork
    91 https://doi.org/10.1016/0021-8693(91)90225-w schema:sameAs https://app.dimensions.ai/details/publication/pub.1031125256
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1016/j.jalgebra.2005.11.023 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029386323
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1016/j.jalgebra.2006.01.053 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040687874
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1063/1.530198 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058107189
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1090/s0894-0347-00-00321-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011296100
    100 rdf:type schema:CreativeWork
    101 https://doi.org/10.1090/s0894-0347-1990-1035415-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027548652
    102 rdf:type schema:CreativeWork
    103 https://doi.org/10.1215/s0012-7094-91-06321-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064419691
    104 rdf:type schema:CreativeWork
    105 https://doi.org/10.1215/s0012-7094-93-06920-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064419839
    106 rdf:type schema:CreativeWork
    107 https://www.grid.ac/institutes/grid.12527.33 schema:alternateName Tsinghua University
    108 schema:name Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China
    109 rdf:type schema:Organization
     




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


    ...