Homogeneous bundles and the trace of the heat kernel

Abstract

AbstractWe study the heat equation on a homogeneous bundle over a compact Lie group. The trace of the heat kernel is explicitly calculated. By comparing this with the formula constructed form the eigenvalues (with multiplicities) of the Laplacian we obtain and unusual formula involving the Clebsch-Gordan numbers. The main method is to use invariance under conjugation to pass from the group to its maximal torus, where a direct calculation can be carried out.