A remark on the simple cuspidal representations of GL(n, F)

Abstract

Let $F$ be a non-archimedean local field of residue characteristic $p$, $G$ be the group $GL(n,F)$. In this note, under the assumption $(n,p)=1$, we show a simple cuspidal representation $\pi$ (that with normalized level $\frac{1}{n}$) of $G$ is determined uniquely up to isomorphism by the local constants of $\chi \circ \text{det}\otimes \pi$ for all characters $\chi$ of $F^{\times }$.

9 pages. This is version 2, and a detailed proof of Lemma 2.2 is included. Submitted

References in corpus (1)

• The Local Langlands Correspondence for Simple Supercuspidal Representations of GL_n(F)

Cited by in corpus (4)

• On the Local Converse Theorem for p-adic GLn
• On the Jacquet Conjecture on the Local Converse Problem for p-adic GL_n
• The Local Langlands Correspondence for Simple Supercuspidal Representations of GL_n(F)
• On a converse theorem for $G_2$ over finite fields