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GAP 3 Package "weyl"The former package WeylThe package "weyl" had already been superseded by the GAP 3 share package "chevie" and hence has not been transferred to GAP 4. Note that "chevie" can only be used under GAP 3. AuthorMeinolf Geck. Implementation
Language: GAP 3 DescriptionThere is a collection of programs for dealing with finite Weyl groups, associated (Iwahori) Hecke algebras, and their representations. These programs were written by Meinolf Geck. On a low level, these programs provide the basic data about a fixed finite Weyl group W: having specified a Cartan matrix, they compute the root system, the reflection representation, and the permutation representation on the root vectors. Elements of W can be given either as permutations or as reduced words in the standard generators (i.e., simply as a list of integers labelling the generators), and there are functions to convert these expressions into each other. In particular, all functions of GAP 3 for working with permutation groups can be applied. On a higher level, it is possible to compute distinguished coset representatives and representatives of the conjugacy classes of W of minimal length. Furthermore, there are functions for calculating KazhdanLusztig polynomials, left cells, and the corresponding representations of the associated Hecke algebra H (for groups of rank <= 5, say). Also, computations inside H are possible, such as multiplying two arbitrary elements of H and expressing the result as a linear combination in the basis elements Tw for w in W. Contact address
Meinolf Geck 