Asymptotics of matrix integrals and tensor invariants of compact Lie groups

Details Asymptotics of matrix integrals and tensor invariants of compact Lie groups Asymptotics of matrix integrals and tensor invariants of compact Lie groups

2006-10-24

arxiv.org/abs/math/0610720v2

Proc. Amer. Math. Soc. 136 (2008), 2235-2244

Mathematics

Representation Theory

final version

Scientific paper

10.1090/S0002-9939-08-09039-4

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 certain operators on the space of tensor invariants, thus extending a result of Biane on the dimension of these spaces.

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