# QGM seminar by Nicolai Reshetikhin (UC Berkeley)

Title: On statistics of irreducible components in large tensor products of modules over simple Lie algebras

2018.11.21 | Jane Jamshidi

 Date Mon 26 Nov Time 15:45 — 16:45 Location 1530-215 (Aud. D3)

Abstract:

Let $V_1,\dots, V_k$ be finite dimensional $\mathfrak g$-modules where $\mathfrak g$ is a finite dimensional Lie algebra and $N_1,\dots, N_k$ are positive integers. In the talk the asymptotical behavior of multiplicities of irreducible representations will be computed in the limit $N_i\to \infty$ with $N_1:\dots: N_k$ being finite. As a consequence the asymptotical probability distribution

of irreducible representations with respect to the Plancherel and other natural probability measures will be established.

Seminar