Group theory aspects of spectral problems on spherical factors
Abstract
The RaySinger isospectral theorem (1971) is applied to a general spectral function for Laplacians of twisted pforms (say) on homogeneous CliffordKlein factors of the threesphere. The inducing formulae necessary to express any spectral quantity for any twisting in terms of those for cyclic subgroups of the tetrahedral, octahedral and icosahedral deck groups are detailed. Further, Artin's theorem allows the McKay correspondence to be obtained. The isospectral theorem is shown to yield a derivation of the Sunada construction which is equivalent to the later one by Pesce.
 Publication:

arXiv eprints
 Pub Date:
 July 2009
 DOI:
 10.48550/arXiv.0907.1309
 arXiv:
 arXiv:0907.1309
 Bibcode:
 2009arXiv0907.1309D
 Keywords:

 Mathematics  Differential Geometry;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Group Theory
 EPrint:
 14 pages