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Representations of Lie groups and random matrices
Author(s):
Benoît
Collins;
Piotr
Sniady
Journal:
Trans. Amer. Math. Soc.
361
(2009),
3269-3287.
MSC (2000):
Primary 22E46;
Secondary 46L53, 15A52
Posted:
January 27, 2009
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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
Sniady
Affiliation:
Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Email:
Piotr.Sniady@math.uni.wroc.pl
DOI:
10.1090/S0002-9947-09-04624-8
PII:
S 0002-9947(09)04624-8
Received by editor(s):
October 10, 2006
Received by editor(s) in revised form:
June 5, 2007, June 26, 2007 and August 22, 2007
Posted:
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 of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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