Journal
DISCRETE MATHEMATICS
Volume 309, Issue 23-24, Pages 6508-6514Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.disc.2009.06.021
Keywords
Hilbert series; Kronecker coefficients; Quantum entanglement; Schur-Weyl duality
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Funding
- University of Wisconsin - Milwaukee, Research Growth Initiative Grant
- National Security Agency grant [H98230-09-0054]
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We compute a stable formula for the Hilbert series of the invariant algebra of polynomial functions on circle times(r)(i=1) C-ni under the action of U(n(1)) x ... x U(n(r)) when viewed as real vector space. This situation has a physical interpretation as it is the quantum analog of an r-particle classical system in which the ith particle has n(i) classical states. The stable formula involves only elementary combinatorics, while its derivation involves the representation theory of the symmetric group. In particular, the Kronecker coefficients play an important role. (C) 2009 Elsevier B.V. All rights reserved.
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