# Cuspidal irreducible complex or l-modular representations of quaternionic forms of p-adic classical groups for odd p

## TL;DR

This paper classifies all cuspidal irreducible representations of quaternionic p-adic classical groups for odd p over algebraically closed fields, establishing their induction from cuspidal types and conjugacy properties.

## Contribution

It provides a complete classification of cuspidal irreducible representations for quaternionic forms of p-adic classical groups, including their construction and conjugacy relations.

## Key findings

- Every cuspidal irreducible representation is induced from a cuspidal type.
- Two intertwining cuspidal types are conjugate under some element of G.
- The classification applies to coefficients in fields of characteristic different from p.

## Abstract

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At first: Every irreducible cuspidal representation of G is induced from a cuspidal type, i.e. from a certain irreducible representation of a compact open subgroup of G, constructed from a beta-extension and a cuspidal representation of a finite group. Secondly we show that two intertwining cuspidal types of G are up to equivalence conjugate under some element of G.