Nicolai Reshetikhin - Statistics of large tensor products of representations of simple Lie algebras

BIMSA-Tsinghua Quantum Symmetry Seminar
2022-12-07
Speaker: Nicolai Reshetikhin (YMSC, BIMSA)

Title:
Statistics of irreducible components in large tensor products of representations of simple Lie algebras

Abstract:
I will explain the solution to the following problem. Given a finite dimensional irreducible representation of a simple Lie algebra, consider its N-th tensor power. It has a decomposition into the direct sum of irreducible modules. The problem is how to find the asymptotic of multiplicities of irreducible subrepresentations in the limit N \to \infty and how to find the asymptotic of the Plancherel and character measures on the set of irreducible components in this limit.

References:
+ work in progress (with O. Postnova and V. Serganova)

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