Asymptotics of matrix integrals and tensor invariants of compact Lie groups
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- by Michael Stolz and Tatsuya Tate PDF
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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.References
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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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2383530