Hecke Algebra Correspondences for the metaplectic group

TL;DR

This paper extends the known correspondence between Bernstein components of Weil representations of the metaplectic group and orthogonal groups from odd to even residual characteristic, broadening the scope of the theory.

Contribution

It generalizes Gan and Savin's result to include cases of even residual characteristic, filling a gap in the existing representation theory.

Findings

Established a correspondence for even residual characteristic

Extended the classification of Bernstein components

Broadened the applicability of metaplectic representation theory

Abstract

Over a p-adic field of odd residual characteristic, Gan and Savin proved a correspondence between the Bernstein components of the even and odd Weil representations of the metaplectic group and the components of the trivial representation of the equal rank odd orthogonal groups. In this paper, we extend their result to the case of even residual characteristic.