Representations of Lie groups and random matrices

Collins, Benoît; Śniady, Piotr

doi:10.1090/S0002-9947-09-04624-8

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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