Computing with Quantized Enveloping Algebras: PBW-Type Bases,Highest-Weight Modules andR-Matrices |
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Affiliation: | Mathematical Institute, University of Utrecht, The Netherlands |
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Abstract: | Let Uq(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 Uq(g). We use this to obtain an algorithm for calculating a Gröbner basis of an ideal in the subalgebra U ? , which leads to a general construction of irreducible highest-weight modules over Uq(g). We also indicate how to compute the corresponding R -matrices. |
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