Automata and cells in affine Weyl groups

Details Automata and cells in affine Weyl groups Automata and cells in affine Weyl groups

2008-07-15

arxiv.org/abs/0807.2463v2

Mathematics

Group Theory

fixed typos

Scientific paper

Let W~ be an affine Weyl group, and let C be a left, right, or two-sided Kazhdan--Lusztig cell in W~. Let Reduced (C) be the set of all reduced expressions of elements of C, regarded as a formal language in the sense of the theory of computation. We show that Reduced (C) is a regular language. Hence the reduced expressions of the elements in any Kazhdan--Lusztig cell can be enumerated by a finite state automaton.

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