An explicit formula for the Dirac multiplicities on lens spaces

@inproceedings{Boldt2014AnEF,
  title={An explicit formula for the Dirac multiplicities on lens spaces},
  author={Sebastian Boldt and Emilio A. Lauret},
  year={2014}
}
  • Sebastian Boldt, Emilio A. Lauret
  • Published 2014
  • Mathematics
  • 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 $\Gamma\backslash \operatorname{Spin}(2m)/\operatorname{Spin}(2m-1)$ and exploiting the representation theory of the $\operatorname{Spin}$ 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… CONTINUE READING

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