2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77664A simplified construction of representations is presented for the quantized enveloping algebra Uq(g), with g being a simple complex Lie algebra belonging to one of the four principal series A, B, C or D. The carrier representation space is the quantized algebra of polynomials in antiholomorphic coordinate functions on the big cell of a coadjoint orbit of K where K is the compact simple Lie group with the Lie algebra g - the compact form of g.AMSTeX file; to appear in Lett. Math. PhysQuantum Algebra17B37; 81R50text