Endoscopic character identities for metaplectic groups

TL;DR

This paper proves the conjectural endoscopic character identities for tempered representations of metaplectic groups, advancing the understanding of their harmonic analysis and representation theory.

Contribution

It establishes the formalism of endoscopic character identities specifically for metaplectic groups, filling a gap in the theory.

Findings

Proved the conjectural endoscopic character identities for $Mp_{2n}$.

Extended endoscopy formalism to metaplectic groups.

Enhanced understanding of harmonic analysis on metaplectic groups.

Abstract

In this paper, we prove the conjectural endoscopic character identities for tempered representations of metaplectic group $Mp_{2n}$ based on the formalism of endoscopy theory by J. Adams, D. Renard and W.W. Li.