Seminar in Representation Theory
Seminar on Char(LG): characters of p-adic groups
2025/10/17 (Fri.) 14:00~15:30
- Date : 2025/10/17 (Fri.) 14:00~15:30
- Location : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
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Speaker : Cheng-Chiang Tsai (AS)
- Abstract :
This is one of the two background talks of the seminar on character sheaves on loop groups. These character sheaves are expected to be similar to and reflect properties of characters of p-adic reductive groups. Harish-Chandra had proved in the 70's that characters of a p-adic reductive groups is locally equal to the Fourier transform of a distribution supported on a nilpotent cone. While the proof is delicate, it is based on a simple idea that when we restrict an irreducible smooth representation to a sufficiently small open compact subgroup, the constituents are "degenerate/nilpotent" in a precise sense.
We will explain characters of p-adic groups, the above simple idea, some heuristic of the full proof, and (if time permits) further enhancements of Moy-Prasad, Waldspurger, DeBacker and Adler-Korman.
(No background on representation theory of p-adic groups will be assumed)
Please see https://idv.sinica.edu.tw/chchtsai/Char(LG)/ for our seminar website.
