Discrete Components of Some Complementary Series (II)
Representation Theory
2013-03-04 v1 Group Theory
Abstract
We show that complementary series of SO(n,1) which are sufficiently close to a cohomological representation in the Fell topology, upon restriction to SO(n-1,1), contain discretely, complementary series for SO(n-1,1) which are also sufficiently close to cohomological representations. As a global application, we show that if the non-zero eigenvalues of the Laplacian for differential forms of middle degree on congruence quotients of the hyperbolic n-space remain bounded away from zero (for all even n), then nonzero eigenvalues of the Laplacian on forms of arbitrary degree remain bonded away from zero; this reduces conjectures of Clozel and Bergeron to the case of middle degree forms.
Cite
@article{arxiv.0905.3140,
title = {Discrete Components of Some Complementary Series (II)},
author = {T. N. Venkataramana B. Speh},
journal= {arXiv preprint arXiv:0905.3140},
year = {2013}
}