Supercuspidal Support of Irreducible Modulo ℓ-Representations of SLn(F)

Abstract

Let $p$ be a prime number and $k$ an algebraically closed field with characteristic $\ell \neq p$. We show that the supercuspidal support of irreducible smooth $k$-representations of Levi subgroups $\textrm {M}^{\prime}$ of $\textrm {SL}_n(F)$ is unique up to $\textrm {M}^{\prime}$-conjugation, where $F$ is either a finite field of characteristic $p$ or a non-Archimedean locally compact field of residual characteristic $p$.