Quantum Frobenius Splittings and Cluster Structures

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-08-05 DOI:10.1007/s10468-024-10281-x

Jinfeng Song

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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量子弗罗贝尼斯分裂和簇结构

我们证明了量子弗罗贝尼乌斯态的对偶及其卢茨蒂格的分裂与量子簇单项式相容。在特殊化之后，我们推导出旗变上的典型弗罗贝尼斯分裂与舒伯特单元上的簇代数结构是兼容的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.