{"title":"Quantum Frobenius Splittings and Cluster Structures","authors":"Jinfeng Song","doi":"10.1007/s10468-024-10281-x","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that the duals of the quantum Frobenius morphisms and their splittings by Lusztig are compatible with quantum cluster monomials. After specialization, we deduce that the canonical Frobenius splittings on flag varieties are compatible with cluster algebra structures on Schubert cells.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-024-10281-x","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 prove that the duals of the quantum Frobenius morphisms and their splittings by Lusztig are compatible with quantum cluster monomials. After specialization, we deduce that the canonical Frobenius splittings on flag varieties are compatible with cluster algebra structures on Schubert cells.
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