Kazhdan-Lusztig cells in planar hyperbolic Coxeter groups and automata

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.

16 pages, 6 figures, v2: revised following referee's comments

References in corpus (2)

• Lusztig's $a$-function for Coxeter groups with complete graphs
• Lusztig's $a$ function for Coxeter groups of rank 3