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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Representations of Lie groups and random matrices
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by Benoît Collins and Piotr Śniady PDF
Trans. Amer. Math. Soc. 361 (2009), 3269-3287 Request permission

Abstract:

We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on representations (for example: tensor product, restriction to a subgroup) correspond to some natural operations on random matrices (respectively: sum of independent random matrices, taking the corners of a random matrix). Our method of proof is to treat the canonical block matrix associated to a representation as a random matrix with non-commutative entries.
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Additional Information
  • Benoît Collins
  • Affiliation: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, Canada K1N 6N5 – and – CNRS, UMR 5208, Institut Camille Jordan, Université Lyon 1, 21 av Claude Bernard, 69622 Villeurbanne, France
  • Email: collins@math.univ-lyon1.fr
  • Piotr Śniady
  • Affiliation: Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
  • Email: Piotr.Sniady@math.uni.wroc.pl
  • Received by editor(s): October 10, 2006
  • Received by editor(s) in revised form: June 5, 2007, June 26, 2007, and August 22, 2007
  • Published electronically: January 27, 2009
  • Additional Notes: The research of the first author was partly supported by a RIMS fellowship and by CNRS
    The research of the second author was supported by State Committee for Scientific Research (KBN) grant \text{2 P03A 007 23}, RTN network: QP-Applications contract No. HPRN-CT-2002-00279, and KBN-DAAD project 36/2003/2004.
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 3269-3287
  • MSC (2000): Primary 22E46; Secondary 46L53, 15A52
  • DOI: https://doi.org/10.1090/S0002-9947-09-04624-8
  • MathSciNet review: 2485426