Probability measure near the boundary of tensor power decomposition for so(2n+1)

TL;DR

This paper analyzes the asymptotic behavior of character measures on irreducible representations of so(2n+1), revealing convergence to a Poisson-type distribution near the boundary of the weight diagram.

Contribution

It provides the first detailed asymptotic analysis of character measures for so(2n+1) near the boundary of the weight diagram.

Findings

Character measure converges to a Poisson-type distribution near the boundary.

Asymptotic formulas for character measures in this regime are derived.

Results enhance understanding of tensor power decompositions in Lie algebra representations.

Abstract

Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fundamental representation. In this paper we calculate the asymptotics of character measure on representations of so(2n+1) in the regime near the boundary of weight diagram. We find out that it converges to a Poisson-type distribution.