Representations of Lie groups and random matrices

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 in corpus (5)

• Character Expansion Methods for Matrix Models of Dually Weighted Graphs
• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• Almost Flat Planar Diagrams
• Gromov-Hausdorff Distance for Quantum Metric Spaces
• The uniqueness question in the multidimensional moment problem with applications to phase space observables

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• Semiclassical asymptotics of ${\mathrm{GL}}_N(\mathbb{C})$ tensor products and quantum random matrices
• Poisson limit theorems for the Robinson-Schensted correspondence and for the multi-line Hammersley process