GAP 3 Package "weyl"

The package "weyl" had already been superseded by the GAP 3 share package "chevie" and hence has not been transferred to GAP 4.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.

Author

Meinolf Geck.

Implementation

Language: GAP 3
Operating system: Any
Current version: Obsolete (in the 3.4.4 distribution)

Description

There 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 Kazhdan-Lusztig 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
Mathematical Sciences
University of Aberdeen
Aberdeen, AB24 3UE
Scotland
email: m.geck@maths.abdn.ac.uk