PyCox: Computing with (finite) Coxeter groups and Iwahori-Hecke algebras

Details PyCox: Computing with (finite) Coxeter groups and Iwahori-Hecke algebras PyCox: Computing with (finite) Coxeter groups and Iwahori-Hecke algebras

2012-01-26

arxiv.org/abs/1201.5566v1

Mathematics

Representation Theory

31 pages

Scientific paper

We introduce the computer algebra package {\sf PyCox}, written entirely in the {\sf Python} language. It implements a set of algorithms - in a spirit similar to the older {\sf 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 groups of rank $\leq 8$ (except $E_8$). Our experiments suggest a re-definition of Lusztig's "special" representations which, conjecturally, should also apply to the unequal parameter case.

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