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

Abstract

AbstractWe 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 andW-graphs, which works efficiently for all finite groups of rank ≤8 (exceptE8). We also discuss the computation of Lusztig’s leading coefficients of character values and distinguished involutions (which works forE8as 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.