曹锡华代数论坛（校级学术报告，地点为理科大楼A504）：

题目： Quantum spherical functions and quantum Pfaffians
演讲人：景乃桓教授（美国北卡洲立大学）
时间：12月22日下午2：45---3：45
摘要：Spherical functions are certain functions on Lie groups which are
invariant under certain subgroups. The zonal spherical functions were first introduced in multivariable complex analysis by L. K. Hua in late 40's and later rediscovered by A. James in early 60's using representation theory of symmetric groups. It was later realized that this part of harmonic analysis can be systemitically generalized for root systems by I. Macdonald and he also introduced the quantized version of zonal symmetric functions.We will study the the spherical functions associated with the quantum homogeneous space of the quantum general linear group modulo the orthogonal subgroup (joint with Yamada) and the symplectic subgroup (joint with Ray). We achieve this by using certain quantum bi-invariants and we also introduce the notion of quantum Pfaffian for the symmetric space. The connection with zonal symmetric polynomials as special Macdonald polynomials will also be discussed.