Bernstein center of supercuspidal blocks

TL;DR

This paper demonstrates that the Bernstein center of a tame supercuspidal block in a tamely ramified reductive group over a local field is isomorphic to that of a depth zero supercuspidal block in a related twisted Levi subgroup, revealing structural similarities.

Contribution

It establishes an isomorphism between the Bernstein centers of tame supercuspidal blocks and depth zero blocks in twisted Levi subgroups, providing new insights into their structure.

Findings

Bernstein center of tame supercuspidal block is isomorphic to that of a depth zero block.

The isomorphism involves a twisted Levi subgroup of the original group.

Results deepen understanding of supercuspidal representations and their centers.

Abstract

Let $\bf{ G}$ 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 $\bf{ G}(k)$ is isomorphic to the Bernstein center of a depth zero supercuspidal block of $\bf{ G}^{0}(k)$ for some twisted Levi subgroup of $\bf{ G}^{0}$ of $\bf{ G}$.