Computing with Quantized enveloping Algebras: PBW-Type Bases, Highest-Weight Modules and R-Matrices

摘要

Let U_q (g) be the quantized enveloping algebra corresponding to the semisimple Lie algebra g. We describe algorithms to obtain the multiplication table of a PBW-type basis of U_q (g). 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 highest-weight modules over U_q (g). We also indicate how to compute the corresponding R-matrices.