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

Rongqing Ye, Elad Zelingher

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.

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

Paper Structure

This paper contains 9 sections, 15 theorems, 120 equations.

Table of Contents

  1. Preliminaries and notation
  2. Notation
  3. The twisted Jacquet-Shalika integral
  4. Simple supercuspidal representations
  5. Computation of the twisted exterior square factors
  6. Preliminary lemmas
  7. The even case
  8. The odd case
  9. Exterior square gamma factors local converse theorem

Key Result

Theorem 1

Let $\pi$ and $\pi'$ be irreducible simple supercuspidal representations of $\mathrm{GL}_{n}\left(F\right)$ sharing the same central character $\omega$, such that $\pi$, $\pi'$ are associated with the data $(t_0, \zeta)$, $(t_0', \zeta')$ respectively. Assume that Suppose for every unitary tamely ra Then $t_0 = t_0'$ and $\zeta = \pm \zeta'$. Moreover, we have $\zeta = \zeta'$ if $n = 2m + 1$ is o

Theorems & Definitions (18)

  • Theorem 1
  • Theorem 1.1: jacquet11exterior
  • Theorem 1.2: jo2018derivatives, CogdellMatringe15
  • Proposition 1.3: ye2018exterior
  • Theorem 1.4: matringe2014linear CogdellMatringe15
  • Theorem 1.5
  • Lemma 1.6
  • Theorem 1.7: knightly2015simple
  • Lemma 2.1
  • Lemma 2.2: ye2018exterior
  • ...and 8 more