Computing with quantized enveloping algebras: PBW-type bases, highest-weight modules, R-matrices

Abstract

Let Uqg be the quantized enveloping algebra corresponding to the semisimple Lie algebra g We describe algorithms to obtain the multiplication table of a PBWtype basis of Uqg We use this to obtain an algorithm for calculating a Grobner basis of an ideal in the subalgebra U which leads to a general construction of irreducible highestweight modules over Uqg We also indicate how to compute the corresponding Rmatrices