On self-dual simple types of $p$-adic classical groups

TL;DR

This paper introduces a new class of simple types called good semisimple strata in p-adic classical groups, extending Bushnell and Kutzko's framework from GL(N,F) to these groups, and defines self-dual simple types.

Contribution

It generalizes the concept of simple types to p-adic classical groups using recent work on semisimple strata, including the novel definition of self-dual simple types.

Findings

Defines good semisimple strata in classical groups.

Constructs simple types analogous to those in GL(N,F).

Introduces self-dual simple types in classical groups.

Abstract

Let $G$ be a classical group over a non-Archimedean local field of odd residual characteristic. Using recent work of S. Stevens, we define a certain kind of semisimple stratum, called good, and show that it provides a simple type in $G$ which is an analogue of the simple type for $GL(N,F)$ defined by Bushnell and Kutzko. Furthermore, we define a self-dual simple type in $G$.