{"title":"Combinatorial description of Lusztig $q$-weight multiplicity","authors":"Seung Jin Lee","doi":"arxiv-2409.02341","DOIUrl":null,"url":null,"abstract":"We conjecture a precise relationship between Lusztig $q$-weight\nmultiplicities for type $C$ and Kirillov-Reshetikhin crystals. We also define\n$\\mathfrak{gl}_n$-version of $q$-weight multiplicity for type $C$ and\nconjecture the positivity.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02341","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We conjecture a precise relationship between Lusztig $q$-weight
multiplicities for type $C$ and Kirillov-Reshetikhin crystals. We also define
$\mathfrak{gl}_n$-version of $q$-weight multiplicity for type $C$ and
conjecture the positivity.
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