Crystal Bases of Modified $\imath $quantum Groups of Certain Quasi-Split Types

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-06-14 DOI:10.1007/s10468-023-10207-z

Hideya Watanabe

引用次数: 0

Abstract

In order to see the behavior of $\imath $canonical bases at $q = \infty $, we introduce the notion of $\imath $crystals associated to an $\imath $quantum group of certain quasi-split type. The theory of $\imath $crystals clarifies why $\imath $canonical basis elements are not always preserved under natural homomorphisms. Also, we construct a projective system of $\imath $crystals whose projective limit can be thought of as the $\imath $canonical basis of the modified $\imath $quantum group at $q = \infty $.

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某些准分裂型修正$$\imath $$量子群的晶体基

为了看清在（q = \infty）处的（（（imath））规范基的行为，我们引入了与（（imath））量子群的某种准分裂类型相关联的（（imath））晶体的概念。$\imath$晶体的理论阐明了为什么$\imath$规范基元在自然同态下并不总是保留的。同时，我们构造了一个投影系统的（（imath）晶体），它的投影极限可以被认为是在（q = \infty \）处的修正量子群的（（imath）规范基础）。

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.

Crystal Bases of Modified \(\imath \)quantum Groups of Certain Quasi-Split Types

Abstract