Tokuyama-type formulas for characters of type B

We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group Spin_2r+1(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 Spin_2r+1(C).