Representations of Lie groups and random matrices

Details Representations of Lie groups and random matrices Representations of Lie groups and random matrices

2006-10-09

arxiv.org/abs/math/0610285v2

Trans. Amer. Math. Soc. 361 (2009), no. 6, 3269--3287

Mathematics

Probability

Scientific paper

10.1090/S0002-9947-09-04624-8

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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