ON MULTIPLICITY-FREE WEIGHT MODULES OVER QUANTUM AFFINE ALGEBRAS

被引：1
作者：
Liu, Xingpeng [1 ]
机构：
[1] Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Shenzhen, Peoples R China
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2024年 / 330卷 / 02期
基金：
中国博士后科学基金;
关键词：
quantum affine algebra; representation theory; multiplicity-free weight modules; OSCILLATOR REPRESENTATIONS; TETRAHEDRON EQUATION; DRINFELD REALIZATION; R MATRICES; CATEGORY;
D O I：
10.2140/pjm.2024.330.251
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Our goal is to construct and study the multiplicity-free weight modules of quantum affine algebras. For this, we introduce the notion of shiftability condition with respect to a symmetrizable generalized Cartan matrix, and investigate its applications on the study of quantum affine algebra structures and the realizations of the infinite-dimensional multiplicity-free weight modules. We also compute the highest `-weights of the infinite-dimensional multiplicity-free weight modules as highest `-weight modules.
引用
收藏
页码：251 / 282
页数：35
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