Bernstein center of supercuspidal blocks

Abstract

Let $\mathbf{G}$ be a tamely ramified connected reductive group defined over a non-archimedean local field $k$. We show that the Bernstein center of a tame supercuspidal block of $\mathbf{G}(\mathbf{k})$ is isomorphic to the Bernstein center of a depth zero supercuspidal block of ${\mathbf{G}}^0(\mathbf{k})$ for some twisted Levi subgroup of ${\mathbf{G}}^0$ of $\mathbf{G}$.

Cited by in corpus (1)

• Hecke algebras for $p$-adic reductive groups and Local Langlands Correspondence for Bernstein blocks