English

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

Representation Theory 2026-05-06 v3 Number Theory

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 new 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. Then, we show that this conjecture is equivalent to the Jiang conjecture on the upper bound of wavefront sets of representations in local Arthur packets and also equivalent to an analogous conjecture on the upper bound of wavefront sets of representations in local ABV packets.

Keywords

Cite

@article{arxiv.2403.11976,
  title  = {On the upper bound of wavefront sets of representations of p-adic groups},
  author = {Alexander Hazeltine and Baiying Liu and Chi-Heng Lo and Freydoon Shahidi},
  journal= {arXiv preprint arXiv:2403.11976},
  year   = {2026}
}

Comments

Added some remarks, references, and made some minor changes. Comments are welcome