Supercuspidal Support of Irreducible Modulo ℓ-Representations of SL<i>n</i>(<i>F</i>)

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 Levi subgroups $\textrm {M}^{\prime}$ {SL}_n(F)$ is unique up to {M}^{\prime}$-conjugation, where $F$ either finite or non-Archimedean locally compact residual $p$.