PyCox: computing with (finite) Coxeter groups and Iwahori-Hecke algebras. 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 E 8 ). We also discuss the computation of Lusztig’s leading coefficients of character values and distinguished involutions (which works for E 8 as well). Our experiments suggest a re-definition of Lusztig’s ‘special’ representations which, conjecturally, should also apply to the unequal parameter case.
Keywords for this software
References in zbMATH (referenced in 7 articles )
Showing results 1 to 7 of 7.
- Yin, Yunchuan: $W$-graph ideals and duality (2016)
- Bonnafé, Cédric; Geck, Meinolf: Hecke algebras with unequal parameters and Vogan’s left cell invariants. (2015)
- Michel, Jean: The development version of the CHEVIE package of GAP3. (2015)
- Yin, Yunchuan: $W$-graphs for Hecke algebras with unequal parameters. (2015)
- Premet, Alexander: Multiplicity-free primitive ideals associated with rigid nilpotent orbits (2014)
- Taylor, Jay: Finding characters satisfying a maximal condition for their unipotent support. (2014)
- Geck, Meinolf: $\mathsfPyCox$: computing with (finite) Coxeter groups and Iwahori-Hecke algebras. (2012)