Kazhdan-Lusztig cells in planar hyperbolic Coxeter groups and automata
Representation Theory
2014-06-23 v2
Abstract
Let C be a one- or two-sided Kazhdan--Lusztig cell in a Coxeter group (W,S), and let Reduced(C) denote the set of reduced expressions of all w in C, regarded as a language over the alphabet S. Casselman has conjectured that Reduced(C) is regular. In this paper we give a conjectural description of the cells when W is the group corresponding to a hyperbolic polygon, and show that our conjectures imply Casselman's.
Cite
@article{arxiv.1212.3274,
title = {Kazhdan-Lusztig cells in planar hyperbolic Coxeter groups and automata},
author = {Mikhail Belolipetsky and Paul Gunnells and Richard Scott},
journal= {arXiv preprint arXiv:1212.3274},
year = {2014}
}
Comments
16 pages, 6 figures, v2: revised following referee's comments