Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Nonzero Kronecker Coefficients and their Consequences for Spectra   A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a
density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A,
r^B, r^{AB}). How can we characterise such triples? It turns out that the
admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with
nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in
Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means
that the irreducible representation V_lambda is contained in the tensor product
of V_mu and V_nu. Here, we show that such triples form a finitely generated
semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are
able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a
complete information-theoretic proof of the correspondence between triples of
spectra and representations. Finally, we show that spectral triples form a
convex polytope.

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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an