Representation Equivalence and p-Spectrum of Constant Curvature Space Forms

Abstract

We study the p-spectrum of a locally symmetric space of constant curvature Γ∖X, in connection with the right regular representation of the full isometry group G of X on (Formula presented.), where τp is the complexified p-exterior representation of O(n) on (Formula presented.). We give an expression of the multiplicity dλ(p,Γ) of the eigenvalues of the p-Hodge–Laplace operator in terms of multiplicities nΓ(π) of specific irreducible unitary representations of G.