Representations of Lie groups and random matrices
Probability
2009-11-06 v2 Representation Theory
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.
Cite
@article{arxiv.math/0610285,
title = {Representations of Lie groups and random matrices},
author = {Benoit Collins and Piotr Sniady},
journal= {arXiv preprint arXiv:math/0610285},
year = {2009}
}