Le lemme fondamental pond\'er\'e pour le groupe m\'etaplectique

TL;DR

This paper proves a weighted fundamental lemma for the metaplectic group, crucial for the stable trace formula, using descent methods under certain conjectural conditions.

Contribution

It establishes a variant of Arthur's lemma for the metaplectic group, advancing the understanding of trace formulas in this context.

Findings

Proves a weighted fundamental lemma for the metaplectic group

Uses descent method under a conjectural fundamental lemma on Lie algebras

Supports the expected validity of the lemma based on prior works

Abstract

We state a variant of Arthur's weighted fundamental lemma for the metaplectic group of Weil, which will be an essential ingredient of the stable trace formula. Over a local field of large enough residual characteristic, we give a proof using the method of descent, which is conditional upon the weighted nonstandard fundamental lemma on Lie algebras. In view of the works of Chaudouard and Laumon, this condition is expected to hold.