{"title":"A tale of two $q$-deformations : connecting dual polar spaces and weighted hypercubes","authors":"Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet","doi":"arxiv-2409.11243","DOIUrl":null,"url":null,"abstract":"Two $q$-analogs of the hypercube graph are introduced and shown to be related\nthrough a graph quotient. The roles of the subspace lattice graph, of a twisted\nprimitive elements of $U_q(\\mathfrak{su}(2))$ and of the dual $q$-Krawtchouk\npolynomials are elaborated upon. This paper is dedicated to Tom Koornwinder.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11243","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
Two $q$-analogs of the hypercube graph are introduced and shown to be related
through a graph quotient. The roles of the subspace lattice graph, of a twisted
primitive elements of $U_q(\mathfrak{su}(2))$ and of the dual $q$-Krawtchouk
polynomials are elaborated upon. This paper is dedicated to Tom Koornwinder.
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