On multiplicities of irreducibles in large tensor product of representations of simple Lie algebras

Olga Postnova, Nicolai Reshetikhin

Published 2018-12-28Version 1

The main result of this paper is the asymptotical formula for multiplicities of irreducible representations in large tensor products of finite dimensional representation of simple Lie algebras. As a consequence we derive the asymptotical distribution of irreducible components in such tensor products where probabilities are given by the natural Plancherel type and character measures. It is interesting that the distribution is universal and after suitable renormalization does not depend on which representations were multiplied.