*主讲人：赵开明 教授（加拿大劳瑞尔大学）
*主持人：胡乃红 教授
*讲座内容简介：
11.10 19:00---20:00 腾讯会议：664 349 812
Title: Simple non-weight representations of affine Kac-Moody algebras
Abstract: Let H be a Cartan subalgebra of an affine Kac-Moody algebra without containing the center. We determine all simple modules on the polynomial algebra C[H] for all affine Kac-Moody algebras. Can we construct some simple modules over A1(1) which are free C[H]-modules of finite rank?
11.12 10:00---11:00 腾讯会议：724 869 536
Title: Simple representations of Witt algebras
Abstract: Some simple non-weight modules over the Witt algebras W_n, W_n^+ and over the Lie algebras sl_n will be constructed from simple modules over the Weyl algebras.
11.12 19:00---20:00 腾讯会议：105 435 435
Title: Simple modules over the Lie algebras of divergence zero vector fields on a torus
Abstract: Let n\ge2 be an integer, Kn the Weyl algebra over the Laurent polynomial algebra An over C in variables x1, x2,…xn, and Sn the Lie algebra of divergence zero vector fields on an n-dimensional torus. For any sln-module V and any module P over Kn, we define an Sn-module structure on the tensor product $P\otimes V$. In this paper, necessary and sufficient conditions for the Sn-modules $P\otimes V$ to be simple are given, and an isomorphism criterion for nonminuscule Sn-modules is provided. More precisely, all nonminuscule Sn-modules are simple, and pairwise nonisomorphic. For minuscule Sn-modules, minimal and maximal submodules are concretely constructed. This is a joint work with B. Dubsky, X. Guo, Y. Yao.
11.15 10:15---11:15 腾讯会议：559 399 542
Title: Irreducible Whittaker modules over the affine Lie algebra $A_1^{(1)}$
Abstract: In 1978, Kostant defined and systematically studied Whittaker modules over an arbitrary finite dimensional complex semisimple Lie algebra$\g$. Recently, Whittaker modules over the various Lie algebra and quantum groups were carefully investigated by many mathematicians. In this talk, irreducible Whittaker modules over the affine Lie algebra $A_1^{(1)}$ will be determined.
*主讲人简介：
赵开明教授，现任加拿大Wilfrid Laurier 大学教授，河北师范大学兼职教授博导。他于 1991 年获得中国科学院数学博士学位; 1994 年至1999 年任中科院数学与系统科学院副研究员；1999年至 2013 年任该研究院研究员。赵开明教授主要研究兴趣为无限维李代数表示理论及非交换代数等科研领域。曾入选中科院早期百人计划。并获得加拿大劳瑞尔大学研究教授荣誉。在 Adv. Math, Trans. AMS, Math. Z. , Moscow J. Math. , J. Algebra 等杂志发表高水平学术论文 140 余篇，被引用1500 多次，主持多项国家自然科学基金项目，及加拿大研究理事会基金项目，是国际代数学领域有重要影响的专家。
