On the metaplectic group in even residual characteristic

TL;DR

This paper explicitly computes the minimal types of the Weil representation for maximal compact subgroups of the metaplectic group in even residual characteristic, extending known results from odd residual characteristic.

Contribution

It provides the first explicit calculation of minimal types in the Schrödinger model for even residual characteristic, broadening the understanding of the Weil representation.

Findings

Explicit formulas for minimal types in even residual characteristic

Extension of known results from odd to even residual characteristic

Enhanced understanding of the structure of the Weil representation

Abstract

For maximal compact subgroups of the metaplectic group, the minimal types in the Schr\"odinger model of the Weil representation are calculated explicitly. Although these types are known in the case of odd residual characteristic, this computation is done for arbitrary residual characteristic.