The fundamental lemma of Jacquet-Rallis in positive characteristics

TL;DR

This paper proves the fundamental lemma for Jacquet-Rallis's relative trace formula in positive characteristic, establishing key cases for both group and Lie algebra versions when the characteristic exceeds the group rank.

Contribution

It provides the first proof of the fundamental lemma in positive characteristic for the Jacquet-Rallis setting, covering both group and Lie algebra cases.

Findings

Proved the fundamental lemma in positive characteristic for the Jacquet-Rallis trace formula.

Established the lemma for both group and Lie algebra versions.

Applicable when the characteristic exceeds the group rank.

Abstract

We prove both the group version and the Lie algebra version of the Fundamental Lemma appearing in a relative trace formula of Jacquet-Rallis in the function field case when the characteristic is greater than the rank of the relevant groups.