报告题目 (Title)： Bailey 格和 Rogers–Ramanujan 恒等式的推广
报告人 (Speaker)：季 青 （天津大学 教授）
报告时间 (Time)：2025年9月19日（周五）10:00
报告地点 (Place)：腾讯会议：251624710
邀请人(Inviter)：陈旦旦
报告摘要：The Rogers–Ramanujan identities, first proved by Rogers in 1894 and rediscovered by Ramanujan a few years later, have found wide-ranging applications across various branches of mathematics. This has led to several generalizations of these two identities, such as a combinatorial generalization by Gordon (now known as the Rogers–Ramanujan–Gordon identities) and an analytic generalization by Andrews. These identities also serve as character formulas in the representation theory of infinite-dimensional Lie algebras and vertex operator algebras.
In this talk, we provide a proof of Bressoud's analytic generalization of the Rogers–Ramanujan identities published in the Memoirs of the American Mathematical Society (1980) using the framework of Bailey lattices. An overpartition analogue of Bressoud's identity is also presented. This is joint work with Thomas Y. He and Alice X. H. Zhao.