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

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'.

arXiv commentThis is the latest version, with notable improvements in writing. Specifically, I've added a case when l=2 in Example 3.11. Section 2 is a part of my thesis arXiv:1912.13473