The MVW involution of the metaplectic group

TL;DR

This paper extends the fundamental MVW involution, originally for classical groups, to the metaplectic group over non-archimedean local fields, broadening its applicability in p-adic representation theory.

Contribution

The authors establish the existence of the MVW involution for the metaplectic group over non-archimedean local fields, generalizing previous results for classical groups.

Findings

MVW involution exists for the metaplectic group over non-archimedean fields

Construction applies to representations over any coefficient field with characteristic not equal to p

Extends duality concepts in p-adic representation theory

Abstract

The MVW involution -- named after Colette Moeglin, Marie-France Vign\'eras, and Jean-Loup Waldspurger -- is a fundamental dualizing involution in the representation theory of $p$-adic classical groups. It extends the well-known transpose-inverse automorphism for general linear groups. In this work, we establish the existence of the MVW involution for the metaplectic group over a non-archimedean local field $F$ of characteristic different from $2$ and with residue characteristic $p$. Our construction applies to representations over any coefficient field of characteristic distinct from $p$.