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PyCox: computing with (finite) Coxeter groups and Iwahori–Hecke algebras

Part of: Special aspects of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  01 August 2012

Meinolf Geck
Meinolf Geck*
Affiliation:
Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom (email: m.geck@abdn.ac.uk)

Abstract

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We introduce the computer algebra package PyCox, written entirely in the Python language. It implements a set of algorithms, in a spirit similar to the older CHEVIE system, for working with Coxeter groups and Hecke algebras. This includes a new variation of the traditional algorithm for computing Kazhdan–Lusztig cells and W-graphs, which works efficiently for all finite groups of rank ≤8 (except E8). We also discuss the computation of Lusztig’s leading coefficients of character values and distinguished involutions (which works for E8 as well). Our experiments suggest a re-definition of Lusztig’s ‘special’ representations which, conjecturally, should also apply to the unequal parameter case. Supplementary materials are available with this article.

MSC classification

Secondary: 20C40: Computational methods 20C08: Hecke algebras and their representations 20F55: Reflection and Coxeter groups
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 231 - 256
Copyright
Copyright © London Mathematical Society 2012

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Supplementary material: File

Geck Supplementary Material

Supplementary Material

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