TY - JOUR

T1 - Asymptotics of matrix integrals and tensor invariants of compact lie groups

AU - Stolz, Michael

AU - Tate, Tatsuya

PY - 2008/6

Y1 - 2008/6

N2 - In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant-theoretic interpretation of this type of integral. For arbitrary regular irreducible representations of arbitrary connected semisimple compact Lie groups, we obtain an asymptotic formula for the trace of permutation operators on the space of tensor invariants, thus extending a result of Biane on the dimension of these spaces.

AB - In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant-theoretic interpretation of this type of integral. For arbitrary regular irreducible representations of arbitrary connected semisimple compact Lie groups, we obtain an asymptotic formula for the trace of permutation operators on the space of tensor invariants, thus extending a result of Biane on the dimension of these spaces.

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U2 - 10.1090/S0002-9939-08-09039-4

DO - 10.1090/S0002-9939-08-09039-4

M3 - Article

AN - SCOPUS:77950660280

SN - 0002-9939

VL - 136

SP - 2235

EP - 2244

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -