Classification on irreducible Whittaker modules over quantum group U_q(sl_3, Λ)

摘要

We define the Whittaker modules over the simply-connected quantum group U-q(sl(3), Lambda); where Lambda is the weight lattice of Lie algebra sl(3): Then we completely classify all those simple ones. Explicitly, a simple Whittaker module over U-q(sl(3), Lambda) is either a highest weight module, or determined by two parameters z is an element of C and gamma is an element of C* (up to a Hopf automorphism).