Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Laplace eigenfunctions on Riemannian symmetric spaces and Borel-Weil
  Theorem   We indicate a geometric relation between Laplace-Beltrami spectra and
eigenfunctions on compact Riemannian symmetric spaces and the Borel-Weil theory
using ideas from symplectic geometry and geometric quantization. This is done
by associating to each compact Riemannian symmetric space, via
Marsden-Weinstein reduction, a generalized flag manifold which covers the space
parametrizing all of its maximal totally geodesic tori. In the process we
notice a direct relation between the Satake diagram of the symmetric space and
the painted Dynkin diagram of its associated flag manifold. We consider in
detail the examples of the classical simply-connected spaces of rank one and
the space SU(3)/SO(3). In the second part of the paper we provide a
construction of harmonic polynomials inducing Laplace-Beltrami eigenfunctions
on the symmetric space from holomorphic sections of the associated line bundle
on the generalized flag manifold. We show that in the examples we consider the
construction provides all of the eigenfunctions.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc