The asymptotic expansion of the heat kernel on a compact Lie group

TL;DR

This paper derives the asymptotic expansion of the heat kernel and heat trace on a compact Lie group using Lie algebra techniques, highlighting the role of the Duflo isomorphism.

Contribution

It provides a new calculation of the heat kernel asymptotics on compact Lie groups employing Lie algebra methods and the Duflo isomorphism.

Findings

Asymptotic expansion of the heat kernel on compact Lie groups derived.

Heat trace asymptotics computed using Lie algebra techniques.

Duflo isomorphism identified as a key tool in the analysis.

Abstract

Let $G$ be a compact connected Lie group equipped with a bi-invariant metric. We calculate the asymptotic expansion of the heat kernel of the laplacian on $G$ and the heat trace using Lie algebra methods. The Duflo isomorphism plays a key role.