Extended Weil representations: the non-dyadic local field cases

TL;DR

This paper investigates Weil representations over non-archimedean local fields with odd residual characteristic, reorganizing them through twisted actions into representations of related covering groups linked to the projective similitude symplectic group.

Contribution

It introduces a novel approach to reorganize Weil representations via twisted actions for non-dyadic local fields, connecting them to projective similitude symplectic groups.

Findings

Reorganization of Weil representations using twisted actions.

Establishment of a connection to $PGMp^{ ext{±}}(W)$ groups.

Extension of known results to non-dyadic local field cases.

Abstract

Let F be a non-archimedean local field of odd residual characteristic. Let W be a symplectic vector space over F. It is known that there are different Weil representations of a Meteplectic covering group Mp(W). By some twisted actions, we reorganize them as a representation of $PGMp^{\pm}(W)$, which is a covering group related to the projective similitude symplectic group.