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Asymptotics of matrix integrals and tensor invariants of compact Lie groups


Authors: Michael Stolz and Tatsuya Tate
Journal: Proc. Amer. Math. Soc. 136 (2008), 2235-2244
MSC (2000): Primary 22E46; Secondary 43A99
DOI: https://doi.org/10.1090/S0002-9939-08-09039-4
Published electronically: February 11, 2008
MathSciNet review: 2383530
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Abstract: 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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Additional Information

Michael Stolz
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, NA 4/32, D-44780 Bochum, Germany
Email: michael.stolz@ruhr-uni-bochum.de

Tatsuya Tate
Affiliation: Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602 Japan
Email: tate@math.nagoya-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-08-09039-4
Keywords: Asymptotic analysis, compact Lie groups, invariant theory, matrix integrals
Received by editor(s): October 19, 2006
Received by editor(s) in revised form: December 12, 2006
Published electronically: February 11, 2008
Communicated by: Mikhail Shubin
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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