Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
$\Gamma\backslash \operatorname{Spin}(2m)/\operatorname{Spin}(2m-1)$ 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 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.

28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess