Cells and representations of right-angled Coxeter groups

Details Cells and representations of right-angled Coxeter groups Cells and representations of right-angled Coxeter groups

2002-06-05

arxiv.org/abs/math/0206035v3

Selecta Math., N. S., 10 (2004), 325--339

Mathematics

Representation Theory

15 pages, 3 figures

Scientific paper

We study Kazhdan-Lusztig cells and the corresponding representations of right-angled Coxeter groups and Hecke algebras associated to them. In case of the infinite groups generated by reflections in the hyperbolic plane about the sides of right-angled polygons we obtain an explicit description of the left and two-sided cells. In particular, we prove that there are infinitely many left cells but they all form only three two-sided cells.

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