Modulo $\ell$-representations of $p$-adic groups $\mathrm{S}{\mathrm{L}}_{\mathrm{n}}(F)$

Abstract

Let $k$ be an algebraically closed field of characteristic $l\ne p$. We construct maximal simple cuspidal $k$-types of Levi subgroups ${\mathrm{M}}^{\prime }$ of ${\mathrm{SL}}_n(F)$, when $F$ is a non-archimedean locally compact field of residual characteristic $p$. We show that the supercuspidal support of irreducible smooth $k$-representations of Levi subgroups ${\mathrm{M}}^{\prime }$ of ${\mathrm{SL}}_n(F)$ is unique up to ${\mathrm{M}}^{\prime }$-conjugation, when $F$ is either a finite field of characteristic $p$ or a non-archimedean locally compact field of residual characteristic $p$.

61 pages