Construction of tame supercuspidal representations in arbitrary residue characteristic

TL;DR

This paper presents a new construction method for supercuspidal representations of reductive groups over nonarchimedean local fields, applicable in all residual characteristics including two, expanding on Yu's earlier work.

Contribution

It introduces a uniform construction of supercuspidal representations that works without Yu's second genericity condition, covering all residual characteristics.

Findings

Includes all Yu's supercuspidal representations

Works in residual characteristic two

Provides a uniform construction method

Abstract

Let F be a nonarchimedean local field whose residue field has at least four elements. Let G be a connected reductive group over F that splits over a tamely ramified field extension of F. We provide a construction of supercuspidal representations of G(F) via compact induction that contains, among others, all the supercuspidal representations constructed by Yu in 2001, but that also works in residual characteristic two. The input for our construction is described uniformly for all residual characteristics and is analogous to Yu's input except that we do not require our input to satisfy the second genericity condition (GE2) that Yu imposes.