Kazhdan-Lusztig cells in planar hyperbolic Coxeter groups and automata

Mikhail Belolipetsky; Paul Gunnells; Richard Scott

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arXiv · 1212.3274

Kazhdan-Lusztig cells in planar hyperbolic Coxeter groups and automata

Mikhail Belolipetsky·Paul Gunnells·Richard Scott

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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.

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BibTeX RIS

Mikhail Belolipetsky, Paul Gunnells, Richard Scott. 2014-06-19. Kazhdan-Lusztig cells in planar hyperbolic Coxeter groups and automata. https://arxiv.org/abs/1212.3274

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