Antiholomorphic representations for orthogonal and symplectic quantum groups

Abstract

The coadjoint orbits for the series $B_l,\ C_l$ and $D_l$ are considered in the case when the base point is a multiple of a fundamental weight. A quantization of the big cell is suggested by means of introducing a $\ast$-algebra generated by holomorphic coordinate functions. Starting from this algebraic structure the irreducible representations of the deformed universal enveloping algebra are derived as acting in the vector space of polynomials in quantum coordinate functions.