Tokuyama-type formulas for type B

Abstract

We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group $\rm{Spin}_{2r+1}({\mathbb C})$, which is an analogue of the formulas of Tokuyama for Schur polynomials and Hamel-King for characters of symplectic groups. To give these, we start with a symplectic group and obtain such characters using the Casselman-Shalika formula. We then analyze this using objects which are naturally attached to the metaplectic double cover of an odd orthogonal group, which also has dual group $\rm{Spin}_{2r+1}({\mathbb C})$.