The Laplacian and the heat kernel acting on differential forms on spheres

Abstract

We show that the Laplacian acting on differential forms on a sphere can be lifted to an operator on its rotation group which is intrinsically equivalent to the Laplacian acting on functions on the Lie group. Further, using the result and the Urakawa summation formula for the heat kernel of the latter Laplacian and the Weyl integration formula, we get a summation formula for the kernel of the former.