dc.contributor.author Boldt, Sebastian dc.contributor.author Lauret, Emilio A. dc.date.accessioned 2016-09-22T10:46:35Z dc.date.available 2016-09-22T10:46:35Z dc.date.issued 2014 dc.identifier.uri http://publications.mfo.de/handle/mfo/188 dc.description OWLF 2013 en_US dc.description.abstract 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 $\Gamma \setminus Spin(2m)/Spin(2m-1)$ and exploiting the representation theory of the Spin groups, we obtain explicit formulas for the multiplicities of the eigenvalues of $D$ in terms of infinitely 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 infinite families of Dirac isospectral lens spaces. These results are complemented by examples found with the help of a computer. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2014,19 dc.subject Dirac spectrum en_US dc.subject Lens spaces en_US dc.subject Isospectrality en_US dc.subject Affine lattices en_US dc.title An Explicit Formula for the Dirac Multiplicities on Lens Spaces en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2014-19 local.scientificprogram OWLF 2013 local.series.id OWP-2014-19 local.subject.msc 58 local.subject.msc 53
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