PROBABILITY MEASURE NEAR THE BOUNDARY OF TENSOR POWER DECOMPOSITION FOR s[o.sub.2n+1]

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 s[o.sub.2n+1] in the regime near the boundary of weight diagram. We find out that it converges to a Poisson-type distribution. Bibliography: 8 titles.
1. INTRODUCTION The probability measures that appear from a decomposition of representation into irreducibles are actively studied for many decades. One of the most famous asymptotic results is the Vershik-Kerov-Logan-Shepp [...]