On the upper bound of wavefront sets of representations of p-adic groups

Alexander Hazeltine, Baiying Liu, Chi-Heng Lo, Freydoon Shahidi

Type: Preprint

Publication Date: 2024-03-18

Citations: 2

DOI: https://doi.org/10.48550/arxiv.2403.11976

Abstract

In this paper we study the upper bound of wavefront sets of irreducible admissible representations of connected reductive groups defined over non-Archimedean local fields of characteristic zero. We formulate a conjecture on the upper bound and show that it can be reduced to that of anti-discrete series representations, namely, those whose Aubert-Zelevinsky duals are discrete series. We also show that this conjecture is equivalent to Jiang's conjecture on the upper bound of wavefront sets of representations in local Arthur packets and also equivalent to an analogue conjecture on the upper bound of wavefront sets of representations in local ABV packets.

Locations

arXiv (Cornell University) - View - PDF

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