Equivariant Dirac operators and differentiable geometric invariant theory

TL;DR

This paper provides a geometric formula for calculating the multiplicities of the equivariant index of a spin-c Dirac operator, advancing the understanding of geometric invariant theory in the context of equivariant index theory.

Contribution

It introduces a new geometric expression for equivariant index multiplicities of spin-c Dirac operators, linking geometric invariant theory with index calculations.

Findings

Derived a geometric formula for equivariant index multiplicities.

Connected geometric invariant theory with Dirac operator analysis.

Enhanced methods for computing equivariant indices in geometric contexts.

Abstract

In this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator.