Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1 ^*

We consider the Plancherel measure on irreducible components of tensor powers spinor representation so(2n+1). The representations correspond to generalized Young diagrams. With respect this probability an is product its multiplicity and dimension, divided by total dimension product. study limit shape diagram when power N rank n algebra tend infinity with N/n fixed. derive explicit formula for prove convergence it in probability. central theorem global fluctuations around shape.