Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Computation of Clebsch-Gordan Coefficients and the Dilation
  Effect   We investigate the problem of computing tensor product multiplicities for
complex semisimple Lie algebras. Even though computing these numbers is #P-hard
in general, we show that if the rank of the Lie algebra is assumed fixed, then
there is a polynomial time algorithm, based on counting the lattice points in
polytopes. In fact, for Lie algebras of type A_r, there is an algorithm, based
on the ellipsoid algorithm, to decide when the coefficients are nonzero in
polynomial time for arbitrary rank. Our experiments show that the lattice point
algorithm is superior in practice to the standard techniques for computing
multiplicities when the weights have large entries but small rank. Using an
implementation of this algorithm, we provide experimental evidence for
conjectured generalizations of the saturation property of
Littlewood--Richardson coefficients. One of these conjectures seems to be valid
for types B_n, C_n, and D_n.

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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin