Representations of Lie groups and random matrices

Benoit Collins; Piotr Sniady

doi:10.1090/s0002-9947-09-04624-8

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arXiv · math/0610285

Representations of Lie groups and random matrices

Benoit Collins·Piotr Sniady

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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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BibTeX RIS

Benoit Collins, Piotr Sniady. 2006-10-09. Representations of Lie groups and random matrices. https://doi.org/10.1090/s0002-9947-09-04624-8

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