The Archimedean Bernstein-Zelevinsky theory
报告人：吴凯迪(The University of Hong Kong)
时间：2025-09-22 15:00-16:30
地点：智华楼 209
The $p$-adic Bernstein-Zelevinsky filtration, developed for smooth representations of general linear groups, has proven highly fruitful in applications to the local Langlands correspondence and branching laws. In this talk, we introduce the Archimedean counterpart of this filtration and outline efforts to generalize it to other classical groups. We then demonstrate how this theory can be employed to provide a first step toward addressing the comparison conjecture. Additionally, we use this framework to provide an affirmative proof of Dipendra Prasad’s conjecture concerning the homological branching laws of the pair $(\GL_{n+1}, \GL_n)$. This is based on a recent joint work with Hongfeng Zhang.
