Automata and cells in affine Weyl groups

Gunnells, Paul

doi:10.1090/S1088-4165-2010-00391-X

Automata and cells in affine Weyl groups
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by Paul E. Gunnells

Represent. Theory 14 (2010), 627-644

DOI: https://doi.org/10.1090/S1088-4165-2010-00391-X

Published electronically: October 1, 2010

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Abstract:

Let $\widetilde {W}$ be an affine Weyl group, and let $C$ be a left, right, or two-sided Kazhdan–Lusztig cell in $\widetilde {W}$. Let $\mathtt {Red}(C)$ 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 $\mathtt {Red}(C)$ 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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