报告题目：On representations of some algebras associated with sl2
报告人：陈洪佳教授（中国科学技术大学）
时 间：2026年4月17日10:00-11:00
地 点：理学院1号楼1-301
摘要：In this talk, we focuses on the representation theory of algebras associated with sl2ℂ, including the affine Lie algebra sl2, the affine Kac-Moody algebra sl2 and the affine-Virasoro algebra Vir⋉sl2. First, we classify certain modules over these algebras, which are free of rank one when restricted to some specific subalgebras. We demonstrate a connection between these modules and modules over the Weyl algebras, which allows us to construct large families of modules that are free of arbitrary finite rank when restricted to the Cartan subalgebra. We then investigate the simplicity of these modules. For reducible modules, we fully characterize their composition factors. Through a comparison with existing simple modules in the literature, we have identified a novel family of simple modules over the affine Kac-Moody algebra sl2. Finally, we turn our attention to a class of tensor product modules over the affine-Virasoro algebra Vir⋉sl2. We derive a necessary and sufficient condition for the simplicity of these modules and determine their isomorphism classes. This talk is based on joint work with Dashu Xu.
报告人简介：陈洪佳，中国科学技术大学数学科学学院教授、博士生导师。2008年在中国科学技术大学获得基础数学博士学位，随后于2008年9月至2014年2月期间，先后在加拿大约克大学、阿尔伯塔大学和劳里埃大学从事学术研究工作。其主要研究方向为无限维李（超）代数与量子群的结构及表示理论。陈洪佳教授主持并参与多项国家自然科学基金项目，曾受邀在全国代数学学术会议及全国李理论学术会议上作大会报告。他在包括Adv. Math., Trans. Amer. Math. Soc., J. Lond. Math. Soc., Math. Z., J. Algebra, J. Pure Appl. Algebra, Nagoya Math. J., Forum Math.等学术期刊上接收发表论文30余篇。
