Character measures in large tensor products of representations of simple Lie algebras

O. V. Postnova^a, N. Yu. Reshetikhin^bcd, V. V. Serganova<sup>e

a</sup> Euler International Mathematical Institute, St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
^b BIMSA, Beijing
^c YMSC, Tsinghua University, Beijing
^d Department of Mathematics and Computer Sciences, St. Petersburg University, Russia
^e Department of Mathematics, University of California, Berkeley, CA 94720, USA

Abstract: We describe the asymptotics of the character measure on irreducible components in large tensor products of the finite dimensional representations of simple Lie algebras with a non-generic argument of characters.

Key words and phrases: Lie algebras, characters, irreducible representations, tensor power decomposition.

Received: 21.12.2025

Language: English