Embeddings Among Quantum Affine sl_(n)

作     者：Yi Qiang LI Yi Qiang LI

作者机构：Department of MathematicsUniversity at BuffaloThe State University of New YorkBuffaloNY 14260USA 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第3期

页      面：792-805页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Partially supported by NSF DMS(Grant No.1801915) 

主　　题：Quantum affine sl_(n) embeddings 

摘      要：We establish an explicit embedding of a quantum affine sl_(n) into a quantum affine sl_(n)+*** embedding serves as a common generalization of two natural,but seemingly unrelated,embed-dings,one on the quantum affine Schur algebra level and the other on the non-quantum *** embedding on the quantum affine Schur algebras is used extensively in the analysis of canonical bases of quantum affine sln and gl_(n).The embedding on the non-quantum level is used crucially in a work of Riche and Williamson on the study of modular representation theory of general linear groups over a finite *** same embedding is also used in a work of Maksimau on the categorical representations of affine general linear *** further provide a more natural compatibility statement of the em-bedding on the idempotent version with that on the quantum affine Schur algebra level.A gl_(n)-variant of the embedding is also established.