Higher rank polynomial modules over U_q(sl_2)

报告主题：Higher rank polynomial modules over U_q(sl_2)
报告时间：2026-05-17 15:30
报告地点：1C207
专家姓名：郭向前
专家简介：郭向前，广州大学数学与信息科学学院教授，博士生导师。2007年毕业于中科院数学所，获理学博士学位，研究方向为李理论及其应用。现为美国《数学评论》评论员，德国《数学文摘》评论员。
报告内容：In this talk, we study the higher rank polynomial modules for the quantum group $U_q(\sl_2)$, improving Bavula's description of irreducible nonweight modules using the terminology of generalized Weyl algebras, constructing examples of irreducible polynomial modules of arbitrary finite rank. Then we consider the tensor products of irreducible polynomial modules with finite-dimensional simple modules, obtaining a direct sum decomposition formula, similar to classical Clebsch-Gordan formula, under some conditions. These results are generalizations of our previous results for the rank-$1$ polynomial modules.