Limit shape for infinite rank limit of non simply-laced Lie algebras of series so(2n+1)

Anton Nazarov, Pavel Nikitin, Olga Postnova

Published 2020-10-30Version 1

We consider the Plancherel measure on irreducible components of tensor powers of spinor representation of so(2n+1). With respect to this measure the probability of an irreducible representation is the product of its multiplicity and its dimension, divided by the total dimension of the tensor product. We study the limit shape of the highest weight when the tensor power and the rank of the algebra tend to infinity at the same rate. We derive the explicit formula for the limit shape and prove convergence of highest weights in probability.