Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable systems on $Fl_n \times Fl_n \times Fl_n //SU(n)$ and $SU(n)$
  tensor product multiplicities   We construct a densely defined torus action on the symplectic quotient of the
product of three complete flag varieties. The closure of the image of the
corresponding moment map is a convex polytope. The dimension of the geometric
quantization of this space gives the structure constants of the representation
ring of $SU(n)$, which we show is given by counting lattice points in the image
of the moment map. Such lattice point formulas for the structure constants were
given by Berenstein-Zelevinsky; our results show how such formulas arise
geometrically as an example of `invariance of polarization', analogous to the
description of the Gelfand-Cetlin polytopes by Guillemin-Sternberg. We outline
applications to loop groups and to moduli spaces of vector bundles.

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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: eess