Hecke algebras and ${\rm SL}_n$-types

Abstract

Let $F$ be a non-Archimedean local field. In an earlier paper, we constructed certain types (in the sense of Bushnell and Kutzko) in $SL_n (F)$, in fact enough to describe the non-supercuspidal components of the Bernstein decomposition of this group. We now give an almost fully explicit presentation of the Hecke algebras of these types.