Borel-Weil-Bott Theorem via Equivariant McKean-Singer Formula

TL;DR

This paper offers a novel proof of the Borel-Weil-Bott theorem by connecting it with index theory, utilizing Kostant's cubic Dirac operator and the equivariant McKean-Singer formula.

Contribution

It introduces a new proof approach for the Borel-Weil-Bott theorem based on index theory and Dirac operators, enriching the theoretical understanding.

Findings

Proof of Borel-Weil-Bott theorem via index theory

Application of Kostant's cubic Dirac operator

Use of equivariant McKean-Singer formula

Abstract

After reviewing how the Borel-Weil-Bott theorem can be interpreted as an index theorem, we present a proof using Kostant's cubic Dirac operator and the equivariant McKean-Singer formula.