Dirac cohomology and character lifting

TL;DR

This paper explores the relationship between Dirac cohomology and character lifting, providing explicit calculations for lifting tempered characters using Dirac index, thereby advancing understanding in representation theory.

Contribution

It introduces a novel approach to character lifting via Dirac cohomology and explicitly computes the transfer of tempered characters.

Findings

Expresses endoscopic transfer factor as difference of spin module characters.

Calculates lifting of tempered characters explicitly using Dirac index.

Links Dirac cohomology with character transfer in representation theory.

Abstract

The endoscopic transfer factor is expressed as difference of characters for the even and odd parts of the spin modules, or Dirac index of the trivial representation. The lifting of tempered characters in terms of index of Dirac cohomology is calculated explicitly.