TY - JOUR
T1 - Asymptotics of matrix integrals and tensor invariants of compact lie groups
AU - Stolz, Michael
AU - Tate, Tatsuya
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
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
VL - 136
SP - 2235
EP - 2244
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 6
ER -