Geometric wave-front set may not be a singleton

TL;DR

This paper demonstrates that for certain supercuspidal representations of ramified p-adic unitary groups, the geometric wave-front set can contain multiple elements, challenging previous assumptions of uniqueness.

Contribution

It reveals that the geometric wave-front set for these representations is not necessarily a singleton, providing new insights into their structure.

Findings

The geometric wave-front set can have multiple elements.

Supercuspidal representations of ramified p-adic unitary groups can have non-singleton wave-front sets.

This challenges prior beliefs about the uniqueness of wave-front sets in this context.

Abstract

We show that the geometric wave-front set of a specific type of supercuspidal representations of ramified $p$-adic unitary groups is not a singleton.