Exterior square gamma factors for cuspidal representations of $\mathrm{GL}_n$: simple supercuspidal representations

TL;DR

This paper computes the local twisted exterior square gamma factors for simple supercuspidal representations of GL_n and establishes a local converse theorem for these representations.

Contribution

It introduces explicit calculations of gamma factors for simple supercuspidal representations and proves a local converse theorem, advancing understanding of these representations.

Findings

Explicit formulas for gamma factors of simple supercuspidal representations.

Proof of a local converse theorem for these representations.

Enhanced classification of simple supercuspidal representations.

Abstract

We compute the local twisted exterior square gamma factors for simple supercuspidal representations, using which we prove a local converse theorem for simple supercuspidal representations.