On depth zero L-packets for classical groups

TL;DR

This paper explicitly constructs Langlands parameters for depth zero irreducible cuspidal representations of classical groups over nonarchimedean fields, extending previous work to non-quasi-split cases and arbitrary tame parameters.

Contribution

It provides a method to determine Langlands parameters for all depth zero cuspidal representations of classical groups, including non-quasi-split cases, and describes associated L-packets explicitly.

Findings

Constructed Langlands parameters for arbitrary depth zero cuspidal representations.

Explicit description of L-packets containing these representations.

Generalized previous results from regular to arbitrary tame parameters.

Abstract

By computing reducibility points of parabolically induced representations, we construct, to within at most two unramified quadratic characters, the Langlands parameter of an arbitrary depth zero irreducible cuspidal representation $\pi$ of a classical group (which may be not-quasi-split) over a nonarchimedean local field of odd residual characteristic. From this, we can explicitly describe all the irreducible cuspidal representations in the union of one, two, or four L-packets, containing $\pi$. These results generalize the work of DeBacker-Reeder (in the case of classical groups) from regular to arbitrary tame Langlands parameters.