Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectra of sub-Dirac operators on certain nilmanifolds   We study sub-Dirac operators that are associated with left-invariant
bracket-generating sub-Riemannian structures on compact quotients of nilpotent
semi-direct products $G=\mathbb{R}^n\rtimes_A\mathbb{R}$. We will prove that
these operators admit an $L^2$-basis of eigenfunctions. Explicit examples show
that the spectrum of these operators can be non-discrete and that eigenvalues
may have infinite multiplicity.

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The categories of this paper are: nlin
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: cs