Representations of the twisted quantized enveloping algebra of type C_n
Abstract
Description
We prove a version of the Poincare-Birkhoff-Witt theorem for the twisted quantized enveloping algebra U'_q(sp_2n). This is a subalgebra of U_q(gl_2n) and a deformation of the universal enveloping algebra U(sp_2n) of the symplectic Lie algebra. We classify finite-dimensional irreducible representations of U'_q(sp_2n) in terms of their highest weights and show that these representations are deformations of the finite-dimensional irreducible representations of sp_2n.
26 pages, extended version, a proof of PBW theorem is added, specialization of modules at q=1 is described, minor corrections are made
26 pages, extended version, a proof of PBW theorem is added, specialization of modules at q=1 is described, minor corrections are made