Representation equivalence and p-spectrum of constant curvature space forms

LAURET, EMILIO AGUSTÍN; MIATELLO, ROBERTO JORGE; ROSSETTI, JUAN PABLO

THE JOURNAL OF GEOMETRIC ANALYSIS

SPRINGER

Año: 2015 vol. 25 p. 564 - 591

1050-6926

We study the p-spectrum of a locally symmetric space of constant curvature GX, in connection with the right regular representation of the full isometry group Iso of X on L^2(GIso)_{tau_p}, where tau_p is the complexified p-exterior representation of O(n) on igwedge^p(R^n)_C.We give an expression of the multiplicity d_{lambda(p,G)} of the eigenvalues of the p-Hodge-Laplace operator in terms of multiplicities n_{G(pi)} of specific irreducible unitary representations of Iso.As a consequence, we extend results of Pesce for the spectrum on functions to the p-spectrum of the Hodge-Laplace operator on p-forms of GX, and we compare p-isospectrality with tau_p-equivalence for 0