|Date||Jul 19, 2016|
Many interesting quantities in Lie theory involve sums over all the elements of a finite Weyl group. The list of them includes the Weyl character formula and the Kostant weight multiplicity formula, which show up in the study of irreducible representations of a semisimple Lie algebra. Another example can be found in the study of affine algebras : the modular S-matrix related to modular transformation properties of affine characters can also be expressed as such a summation. Thus it is sometimes useful to know how to generate all elements of a given finite Weyl group and work with them explicitly using computers. I will explain some basic ideas together with computer demonstrations.