Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quaternionic spherical harmonics and a sharp multiplier theorem on
  quaternionic spheres   A sharp $L^p$ spectral multiplier theorem of Mihlin--H\"ormander type is
proved for a distinguished sub-Laplacian on quaternionic spheres. This is the
first such result on compact sub-Riemannian manifolds where the horizontal
space has corank greater than one. The proof hinges on the analysis of the
quaternionic spherical harmonic decomposition, of which we present an
elementary derivation.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph