The Polynomial Modules over Quantum Group Uq(sl3).

Let g be a finite dimensional complex simple Lie algebra with Cartan subalgebra h. Then C [ h ] has a g -module structure if and only if g is of type A or of type C ; this is called the polynomial module of rank one. In the quantum version, the rank one polynomial modules over U q (sl 2) have been classified. In this paper, we prove that the quantum group U q (sl 3) has no rank one polynomial module. [ABSTRACT FROM AUTHOR]