On the uniqueness of generic representations in an $L$-packet

TL;DR

This paper provides a concise proof demonstrating the uniqueness of generic representations within an $L$-packet for certain classical groups over non-archimedean local fields, clarifying a key aspect of the local Langlands correspondence.

Contribution

The paper introduces a simplified proof of the uniqueness of generic representations in $L$-packets for quasi-split classical groups, enhancing understanding of their structure.

Findings

Proves the uniqueness of generic representations in $L$-packets.

Simplifies previous proofs with a more concise argument.

Clarifies the structure of $L$-packets for classical groups.

Abstract

In this paper, we give a simple and short proof of the uniqueness of generic representations in an $L$-packet for a quasi-split connected classical group over a non-archimedean local field.