Quantum Twist Maps and Dual Canonical Bases View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-06

AUTHORS

Yoshiyuki Kimura, Hironori Oya

ABSTRACT

In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the “reverse” lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors. More... »

PAGES

589-604

References to SciGraph publications

  • 2010. Introduction to Quantum Groups in NONE
  • 1997-05. Total positivity in Schubert varieties in COMMENTARII MATHEMATICI HELVETICI
  • 2013-05. Cluster structures on quantum coordinate rings in SELECTA MATHEMATICA
  • 2015-10. Quantum cluster characters of Hall algebras in SELECTA MATHEMATICA
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10468-017-9729-5

    DOI

    http://dx.doi.org/10.1007/s10468-017-9729-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1091351240


    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": "Osaka Prefecture University", 
              "id": "https://www.grid.ac/institutes/grid.261455.1", 
              "name": [
                "Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, 599-8531, Sakai, Osaka, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kimura", 
            "givenName": "Yoshiyuki", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Tokyo", 
              "id": "https://www.grid.ac/institutes/grid.26999.3d", 
              "name": [
                "Graduate School of Mathematical Sciences, The University of Tokyo, 153-8914, Komaba, Tokyo, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Oya", 
            "givenName": "Hironori", 
            "id": "sg:person.013514255415.83", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013514255415.83"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/pl00000363", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010317247", 
              "https://doi.org/10.1007/pl00000363"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1006/aima.1996.0057", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016599282"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00029-012-0099-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021542189", 
              "https://doi.org/10.1007/s00029-012-0099-x"
            ], 
            "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/10.1090/s0894-0347-99-00295-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037489853"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.aim.2013.07.008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038254969"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00029-014-0177-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039156923", 
              "https://doi.org/10.1007/s00029-014-0177-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1006/aima.1996.0061", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049718648"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-0-8176-4717-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051089613", 
              "https://doi.org/10.1007/978-0-8176-4717-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-0-8176-4717-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051089613", 
              "https://doi.org/10.1007/978-0-8176-4717-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0894-0347-2011-00715-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059339389"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/21562261-1550976", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064414756"
            ], 
            "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/s0012-7094-93-07131-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064419896"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/s0012-7094-99-09915-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064420550"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/crelle-2016-0046", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1067528158"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2140/pjm.2017.286.125", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069072980"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2977/prims/1195166130", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1070934610"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/memo/1169", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084177495"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1112/jlms.12059", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1090276612"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2018-06", 
        "datePublishedReg": "2018-06-01", 
        "description": "In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincar\u00e9-Birkhoff-Witt type bases under the \u201creverse\u201d lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s10468-017-9729-5", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.6080486", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.5856433", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1136385", 
            "issn": [
              "1386-923X", 
              "1572-9079"
            ], 
            "name": "Algebras and Representation Theory", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "21"
          }
        ], 
        "name": "Quantum Twist Maps and Dual Canonical Bases", 
        "pagination": "589-604", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "08a514d2a16ed3f4353a083f57d651d0a6ff38db0f536ad086e3f32ab99a0c97"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10468-017-9729-5"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1091351240"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10468-017-9729-5", 
          "https://app.dimensions.ai/details/publication/pub.1091351240"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T09:59", 
        "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/v90/0000000347_0000000347/records_89814_00000003.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs10468-017-9729-5"
      }
    ]
     

    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/s10468-017-9729-5'

    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/s10468-017-9729-5'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10468-017-9729-5'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10468-017-9729-5'


     

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

    135 TRIPLES      21 PREDICATES      46 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10468-017-9729-5 schema:about anzsrc-for:02
    2 anzsrc-for:0206
    3 schema:author N3726bf307dc44a07b810c6a58ef47934
    4 schema:citation sg:pub.10.1007/978-0-8176-4717-9
    5 sg:pub.10.1007/pl00000363
    6 sg:pub.10.1007/s00029-012-0099-x
    7 sg:pub.10.1007/s00029-014-0177-3
    8 https://doi.org/10.1006/aima.1996.0057
    9 https://doi.org/10.1006/aima.1996.0061
    10 https://doi.org/10.1016/j.aim.2013.07.008
    11 https://doi.org/10.1090/memo/1169
    12 https://doi.org/10.1090/s0894-0347-1990-1035415-6
    13 https://doi.org/10.1090/s0894-0347-2011-00715-7
    14 https://doi.org/10.1090/s0894-0347-99-00295-7
    15 https://doi.org/10.1112/jlms.12059
    16 https://doi.org/10.1215/21562261-1550976
    17 https://doi.org/10.1215/s0012-7094-91-06321-0
    18 https://doi.org/10.1215/s0012-7094-93-07131-1
    19 https://doi.org/10.1215/s0012-7094-99-09915-5
    20 https://doi.org/10.1515/crelle-2016-0046
    21 https://doi.org/10.2140/pjm.2017.286.125
    22 https://doi.org/10.2977/prims/1195166130
    23 schema:datePublished 2018-06
    24 schema:datePublishedReg 2018-06-01
    25 schema:description In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the “reverse” lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors.
    26 schema:genre research_article
    27 schema:inLanguage en
    28 schema:isAccessibleForFree true
    29 schema:isPartOf N7e6a1baac62d48cb982136ab7e5b9b5a
    30 Nac29df3127b64916afb721bd4ae56298
    31 sg:journal.1136385
    32 schema:name Quantum Twist Maps and Dual Canonical Bases
    33 schema:pagination 589-604
    34 schema:productId N48391e79233e40d8bdc6131732df72dc
    35 N93c051c8e2cd4803ba9183e9e5459e07
    36 Na6b011a10ae341de80e67802040515a4
    37 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091351240
    38 https://doi.org/10.1007/s10468-017-9729-5
    39 schema:sdDatePublished 2019-04-11T09:59
    40 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    41 schema:sdPublisher Ned5783574400455a89993c75c0900717
    42 schema:url https://link.springer.com/10.1007%2Fs10468-017-9729-5
    43 sgo:license sg:explorer/license/
    44 sgo:sdDataset articles
    45 rdf:type schema:ScholarlyArticle
    46 N3726bf307dc44a07b810c6a58ef47934 rdf:first Nf11ae55248a44263b8333511c6e88db0
    47 rdf:rest N741d578ae4474619b098d5d64cb0138e
    48 N48391e79233e40d8bdc6131732df72dc schema:name readcube_id
    49 schema:value 08a514d2a16ed3f4353a083f57d651d0a6ff38db0f536ad086e3f32ab99a0c97
    50 rdf:type schema:PropertyValue
    51 N741d578ae4474619b098d5d64cb0138e rdf:first sg:person.013514255415.83
    52 rdf:rest rdf:nil
    53 N7e6a1baac62d48cb982136ab7e5b9b5a schema:issueNumber 3
    54 rdf:type schema:PublicationIssue
    55 N93c051c8e2cd4803ba9183e9e5459e07 schema:name dimensions_id
    56 schema:value pub.1091351240
    57 rdf:type schema:PropertyValue
    58 Na6b011a10ae341de80e67802040515a4 schema:name doi
    59 schema:value 10.1007/s10468-017-9729-5
    60 rdf:type schema:PropertyValue
    61 Nac29df3127b64916afb721bd4ae56298 schema:volumeNumber 21
    62 rdf:type schema:PublicationVolume
    63 Ned5783574400455a89993c75c0900717 schema:name Springer Nature - SN SciGraph project
    64 rdf:type schema:Organization
    65 Nf11ae55248a44263b8333511c6e88db0 schema:affiliation https://www.grid.ac/institutes/grid.261455.1
    66 schema:familyName Kimura
    67 schema:givenName Yoshiyuki
    68 rdf:type schema:Person
    69 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
    70 schema:name Physical Sciences
    71 rdf:type schema:DefinedTerm
    72 anzsrc-for:0206 schema:inDefinedTermSet anzsrc-for:
    73 schema:name Quantum Physics
    74 rdf:type schema:DefinedTerm
    75 sg:grant.5856433 http://pending.schema.org/fundedItem sg:pub.10.1007/s10468-017-9729-5
    76 rdf:type schema:MonetaryGrant
    77 sg:grant.6080486 http://pending.schema.org/fundedItem sg:pub.10.1007/s10468-017-9729-5
    78 rdf:type schema:MonetaryGrant
    79 sg:journal.1136385 schema:issn 1386-923X
    80 1572-9079
    81 schema:name Algebras and Representation Theory
    82 rdf:type schema:Periodical
    83 sg:person.013514255415.83 schema:affiliation https://www.grid.ac/institutes/grid.26999.3d
    84 schema:familyName Oya
    85 schema:givenName Hironori
    86 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013514255415.83
    87 rdf:type schema:Person
    88 sg:pub.10.1007/978-0-8176-4717-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051089613
    89 https://doi.org/10.1007/978-0-8176-4717-9
    90 rdf:type schema:CreativeWork
    91 sg:pub.10.1007/pl00000363 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010317247
    92 https://doi.org/10.1007/pl00000363
    93 rdf:type schema:CreativeWork
    94 sg:pub.10.1007/s00029-012-0099-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1021542189
    95 https://doi.org/10.1007/s00029-012-0099-x
    96 rdf:type schema:CreativeWork
    97 sg:pub.10.1007/s00029-014-0177-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039156923
    98 https://doi.org/10.1007/s00029-014-0177-3
    99 rdf:type schema:CreativeWork
    100 https://doi.org/10.1006/aima.1996.0057 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016599282
    101 rdf:type schema:CreativeWork
    102 https://doi.org/10.1006/aima.1996.0061 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049718648
    103 rdf:type schema:CreativeWork
    104 https://doi.org/10.1016/j.aim.2013.07.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038254969
    105 rdf:type schema:CreativeWork
    106 https://doi.org/10.1090/memo/1169 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084177495
    107 rdf:type schema:CreativeWork
    108 https://doi.org/10.1090/s0894-0347-1990-1035415-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027548652
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1090/s0894-0347-2011-00715-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059339389
    111 rdf:type schema:CreativeWork
    112 https://doi.org/10.1090/s0894-0347-99-00295-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037489853
    113 rdf:type schema:CreativeWork
    114 https://doi.org/10.1112/jlms.12059 schema:sameAs https://app.dimensions.ai/details/publication/pub.1090276612
    115 rdf:type schema:CreativeWork
    116 https://doi.org/10.1215/21562261-1550976 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064414756
    117 rdf:type schema:CreativeWork
    118 https://doi.org/10.1215/s0012-7094-91-06321-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064419691
    119 rdf:type schema:CreativeWork
    120 https://doi.org/10.1215/s0012-7094-93-07131-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064419896
    121 rdf:type schema:CreativeWork
    122 https://doi.org/10.1215/s0012-7094-99-09915-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064420550
    123 rdf:type schema:CreativeWork
    124 https://doi.org/10.1515/crelle-2016-0046 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067528158
    125 rdf:type schema:CreativeWork
    126 https://doi.org/10.2140/pjm.2017.286.125 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069072980
    127 rdf:type schema:CreativeWork
    128 https://doi.org/10.2977/prims/1195166130 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070934610
    129 rdf:type schema:CreativeWork
    130 https://www.grid.ac/institutes/grid.261455.1 schema:alternateName Osaka Prefecture University
    131 schema:name Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, 599-8531, Sakai, Osaka, Japan
    132 rdf:type schema:Organization
    133 https://www.grid.ac/institutes/grid.26999.3d schema:alternateName University of Tokyo
    134 schema:name Graduate School of Mathematical Sciences, The University of Tokyo, 153-8914, Komaba, Tokyo, Japan
    135 rdf:type schema:Organization
     




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


    ...