Based modules over the $$\imath $$quantum group of type AI
Based modules over the $$\imath $$quantum group of type AI
复制标题
基于 AI 类型 $$imath $$quantum 组的模块
DOI：
10.1007/s00209-022-03189-z
复制
发表时间：
2023
影响因子：
0.8
通讯作者：
Watanabe Hideya
中科院分区：
文献类型：
--
作者：
川島朋也;澁澤柊花;天野薫;Yusuke Nakajima;Watanabe Hideya
本文研究AI型量子群上的经典权模。我们通过推广量子群（量子包络代数）上的基模的概念引入基模的概念。证明了每一个最高权为整数的有限维不可约经典权模都是基模。作为副产品，得到了一个新的组合公式的分支规则从。
This paper studies classical weight modules over thequantum groupof type AI. We introduce the notion of based-modules by generalizing the notion of based modules over quantum groups (quantized enveloping algebras). We prove that each finite-dimensional irreducible classical weight-module with integer highest weight is a based-module. As a byproduct, a new combinatorial formula for the branching rule fromtois obtained.