l-modular representations of p-adic groups SLn(F): maximal simple k-types

TL;DR

This paper constructs and classifies maximal simple k-types for Levi subgroups of SLn(F) over non-archimedean fields, extending the understanding of modular representations in p-adic groups.

Contribution

It introduces a method to construct maximal simple k-types for Levi subgroups of SLn(F) and proves their uniqueness up to conjugacy, advancing modular representation theory.

Findings

Constructed maximal simple k-types for Levi subgroups of SLn(F).

Proved the unicity of intertwining implies conjugacy for these types.

Extended the classification to simple k-characters of M'.

Abstract

Let p be an arbitrary prime number and k be an algebraically closed field of characteristic l different from p. We construct maximal simple k-types of Levi subgroups M' of SLn(F), when F is a non-archimedean locally compact field of residual characteristic p, which is to say that any cuspidal k-representation of M' can be compactly induced from an irreducible k-representation of a compact modulo centre subgroup of M', and we also prove the unicity property of intertwining implies conjugacy for maximal simple k-types, extended maximal simple k-types and simple k-characters of M'.