Irreducibility of wave-front sets for depth zero cuspidal representations
Representation Theory
2023-10-18 v2
Abstract
We show that the results of [BM97, DeB02b, Oka, Lus85, AA07, Tay16] imply a positive answer to the question of Moeglin-Waldspurger on wave-front sets in the case of depth zero cuspidal representations. Namely, we deduce that for large enough residue characteristic, the Zariski closure of the wave-front set of any depth zero irreducible cuspidal representation of any reductive group over a non-Archimedean local field is an irreducible variety. In more details, we use [BM97, DeB02b, Oka] to reduce the statement to an analogous statement for finite groups of Lie type, which is proven in [Lus85, AA07, Tay16].
Keywords
Cite
@article{arxiv.2205.14695,
title = {Irreducibility of wave-front sets for depth zero cuspidal representations},
author = {Avraham Aizenbud and Dmitry Gourevitch and Eitan Sayag},
journal= {arXiv preprint arXiv:2205.14695},
year = {2023}
}
Comments
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