Stability of $$\imath $$ canonical Bases of Locally Finite Type

IF 0.4 3区数学 Q4 MATHEMATICS

Transformation Groups Pub Date : 2024-09-14 DOI:10.1007/s00031-024-09876-x

Hideya Watanabe

引用次数: 0

Abstract

We prove the stability conjecture of $\imath $canonical bases, which was raised by Huanchen Bao and Weiqiang Wang in 2016, for all locally finite types. To this end, we characterize the trivial module over the $\imath $quantum groups of such type at $q = \infty $. This result can be seen as a very restrictive version of the $\imath $crystal base theory for locally finite types.

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局部有限类型的 $$\imath $$ 规范基础的稳定性

我们证明了包焕臣和王伟强在 2016 年提出的针对所有局部有限类型的 $\imath$canonical bases 的稳定性猜想。为此，我们表征了在 $q = \infty $时这种类型的 $\imath $量子群上的琐碎模块。这个结果可以被看作是局部有限类型的晶体基础理论的一个限制性版本。

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

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.