Index character associated to the projective Dirac operator

TL;DR

This paper derives an equivariant index formula for an infinite dimensional Clifford module linked to Riemannian manifolds, generalizing the fractional index formula of the projective Dirac operator.

Contribution

It introduces a new equivariant index formula for an infinite dimensional Clifford module, extending previous fractional index results by Mathai--Melrose--Singer.

Findings

Derived a comprehensive equivariant index formula for the Clifford module.

Unified the fractional index formula within a broader framework.

Provided mathematical tools for analyzing projective Dirac operators.

Abstract

We calculate the equivariant index formula for an infinite dimensional Clifford module canonically associated to any Riemannian manifold. It encompasses the fractional index formula of the projective Dirac operator by Mathai--Melrose--Singer.