Irreducibility of wave-front sets for depth zero cuspidal representations

Avraham Aizenbud; Dmitry Gourevitch; Eitan Sayag

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arXiv · 2205.14695

Irreducibility of wave-front sets for depth zero cuspidal representations

Avraham Aizenbud·Dmitry Gourevitch·Eitan Sayag

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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].

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Avraham Aizenbud, Dmitry Gourevitch, Eitan Sayag. 2023-10-17. Irreducibility of wave-front sets for depth zero cuspidal representations. https://arxiv.org/abs/2205.14695

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