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

Modulo $\ell$-representations of $p$-adic groups $\mathrm{SL_n}(F)$