中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
表示论研讨班
Speaker: 张健 教授（华中师范大学）
Inviter: 方明
Language: Chinese
Title: Gelfand-Tetlin bases for quantum groups at root of unity
Time & Venue: 2026年6月23日（星期二）10: 00 - 11: 00 & 思源楼 S425
Abstract: One of the central problems of representation theory is to construct a basis in the representation space and to find the representation matrices in the basis. A solution of this problem for the general linear Lie algebra and the orthogonal Lie algebra was given by Gelfand and Tsetlin. Their method has since been generalized to various other algebras, including Lie superalgebras, Yangians, finite W-algebras, and quantum groups. In this talk, we will present the construction of Gelfand-Tsetlin basis for quantum groups at root of unity. We construct explicit bases for the representation spaces and describe the action of the generators on these basis vectors. This talk is based on joint work with Hao Chang and Ruiying Hou.
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