The spectrum of the Laplacian on forms over a Lie group

Howard D. Fegan

Vol. 90 (1980), No. 2, 373–387

DOI: 10.2140/pjm.1980.90.373

Abstract

Let G be a compact, semi-simple, connected and simply connected Lie group. Then the bundle of p-forms, denoted by Ω^p has a Laplacian Δ : Ω^p → Ω^p defined by the Riemannian structure on G. Then the problem of finding the eigenforms and corresponding eigenvalues is considered in this paper. Our solution is given in terms of the representation theory of G and is contained in the following.

Mathematical Subject Classification 2000

Primary: 58G25

Secondary: 22E70, 58A14, 10D40

Milestones

Received: 6 February 1979

Published: 1 October 1980