Number Theory Seminar

Seminar information archive ~05/02Next seminarFuture seminars 05/03~

Date, time & place Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Naoki Imai, Shane Kelly

2024/11/27

17:00-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Kaito Masuzawa (University of Tokyo)
On the correspondence of simple supercuspidal representations of $\mathrm{GSp}_{2n}$ and its inner form (Japanese)
[ Abstract ]
Let $F$ be a nonarchimedean local field. The local Jacquet-Langlands correspondence is the one-to-one correspondence of essential square integrable representations of $\mathrm{GL}_n(F)$ and its inner form. It is known that this correspondence satisfies the character relation and preserves the simple supercuspidality. We assume the correspondence of simple supercuspidal representations of $\mathrm{GSp}_{2n}(F)$ and irreducible admissible representations of its inner form which satisfies the character relation. This is expected to exist by a standard argument using the theory of stable trace formula. In this talk, we show the simple supercuspidality is preserved under this correspondence. In addition, we can parametrize simple supercuspidal representations and describe the correspondence explicitly.