Commutation of transfer and Aubert-Zelevinski involution for metaplectic groups

TL;DR

This paper extends a known compatibility result between endoscopic transfer and Aubert-Zelevinski involution from linear groups to metaplectic groups, broadening the understanding of these involutions in more complex settings.

Contribution

It generalizes Hiraga's compatibility result to the setting of metaplectic groups, which are a class of non-linear covering groups.

Findings

Endoscopic transfer is compatible with Aubert-Zelevinski involution for metaplectic groups.

The generalization broadens the applicability of known involution properties.

Provides foundational results for further research in metaplectic representation theory.

Abstract

A result of K. Hiraga says endoscopic transfer is compatible with Aubert-Zelevinski involution. In this short note, we generalize Hiraga's result to metaplectic group setting.