Representations of unipotent reduction for SO(2n+1), II: endoscopy

TL;DR

This paper investigates the endoscopic identities of unipotent reduction representations for SO(2n+1) over p-adic fields, confirming Lusztig's parametrization and advancing understanding of their structure.

Contribution

It proves that the tempered irreducible unipotent reduction representations satisfy the expected endoscopic identities, validating Lusztig's parametrization for these groups.

Findings

Confirmed endoscopic identities for unipotent reduction representations.

Validated Lusztig's parametrization of these representations.

Enhanced understanding of the structure of SO(2n+1) representations.

Abstract

For the groups SO(2n+1,F), where F is a p-adic field, we consider the tempered irr{\'e}ducible representations of unipotent reduction. Lusztig has contructed and parametrized these representations. We prove that they satisfy the expected endoscopic identities which determine the parametrization.