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