## 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.## References

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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