Seminar in Representation Theory
Schwartz Algebra Structures in Smooth Casselman-Jacquet Theory
2026/08/19 (Wed.) 10:00~11:30
- Date : 2026/08/19 (Wed.) 10:00~11:30
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
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Speaker : Kei Yuen Chan (University of Hong Kong)
- Organizer : Chun-Ju Lai (AS)
- Abstract :
The smooth Casselman–Jacquet functor is a systematic tool for studying the restriction of representations of a reductive group to its parabolic subgroups. Roughly speaking, this functor is adjoint to parabolic induction. Our approach of investigating the functor combines analytic and algebraic perspectives, with the Schwartz algebra of a nilpotent Lie algebra playing a central role.
In this talk, I will explain how to establish, for Schwartz algebras, analogues of several fundamental results from commutative algebra, including Nakayama's lemma, the Artin–Rees lemma, and the Krull intersection theorem. I will then show how these results imply desirable properties of the smooth Casselman–Jacquet functor, and how they lead to a real-group analogue of Bernstein–Zelevinsky filtrations.
This is based on recent joint work with Kaidi Wu, Jun Yu, and Hongfeng Zhang.
Time permitting, I will also discuss computation aspects of Bernstein-Zelevinsky theory, in connections with p-adic groups.
