报 告 人： 张之正 教授（洛阳师范学院）
报告题目：Multiple Basic Hypergeometric Series and Mock Theta Functions
报告时间：本周三（2018.8.29）下午15:30 - 16：30
The theory of basic hypergeometric series consists of many known summationand transformation formulas. These basic hypergeometric series identitiesfrequently appear in combinatorics and in related area such as number theory,physics, and representation theory of Lie algebras. Multiple basic hypergeometricseries associated to the unitary group $A_n$ (or$U(n+1)$), $C_n$ and $D_n$ have been investigated by various authors. Many different types of such series exist in the literature. In this talk, we give
1. $U(n+1)$ analogue of AAB Bailey lattice (Agarwal, Andrews and Bressoud) and its applications.
2. $U(n+1)$, $C_n$ and elliptic generalizations of WP-Bailey pairs and their applications.
3. A WP-Bailey lattices and its $U(n+1)$ analogue.
4. Mock theta functions in terms of $q$-hypergeometric double sums.