Emilio A. Lauret

Spectra of Lens Spaces from 1-Norm Spectra of Congruence Lattices

Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Cordoba. Centro de Investigacion y Estudios de Matematica. Universidad Nacional de Cordoba. Centro de Investigacion y Estudios de Matematica; Argentina

An Explicit Formula for the Dirac Multiplicities on Lens Spaces

We present a new description of the spectrum of the (spin-) Dirac operator D on lens spaces. Viewing a spin lens space L as a locally symmetric space

Representation Equivalence and p-Spectrum of Constant Curvature Space Forms

\Gamma \backslash {\text {Spin}}(2m)/{\text {Spin}}(2m-1)

Non-strongly isospectral spherical space forms

Γ\Spin(2m)/Spin(2m-1) and exploiting the representation theory of the

On the SO(n + 3) to SO(n) branching multiplicity space

{\text {Spin}}

A numerical study on exceptional eigenvalues of certain congruence subgroups of SO(n, 1) and SU(n, 1)

Spin groups, we obtain explicit formulas for the multiplicities of the eigenvalues of D in terms of finitely many integer operations. As a consequence, we present conditions for lens spaces to be Dirac isospectral. Tackling classic questions of spectral geometry, we prove with the tools developed that neither spin structures nor isometry classes of lens spaces are spectrally determined by giving infinitely many examples of finite families of Dirac isospectral lens spaces. These results are complemented by examples found with the help of a computer.