Q-DEFORMED VERMA REPRESENTATIONS OF QUANTUM ALGEBRA SLQ(3) AND NEW TYPE YANG-BAXTER MATRICES

The q-deformation of Verma theory for the Lie algebra is studied in this paper. The indecomposable representations and the induced representations of quantum universal enveloping algebra sl(q)(3) are constructed on the q-deformed Verma space and the quotient spaces respectively. We put stress on the discussion of the case in which q is a root of unity. Using the new representation constrained in the subalgebra sl(q)(2), we systematically construct the new series of solutions (Yang-Baxter matrices) for Yang-Baxter equation without spectral parameter.