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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Automata and cells in affine Weyl groups
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by Paul E. Gunnells PDF
Represent. Theory 14 (2010), 627-644 Request permission

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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Additional Information
  • Paul E. Gunnells
  • Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003
  • Email: gunnells@math.umass.edu
  • Received by editor(s): September 5, 2008
  • Received by editor(s) in revised form: July 27, 2009
  • Published electronically: October 1, 2010
  • © Copyright 2010 American Mathematical Society
  • Journal: Represent. Theory 14 (2010), 627-644
  • MSC (2010): Primary 20F10, 20F55
  • DOI: https://doi.org/10.1090/S1088-4165-2010-00391-X
  • MathSciNet review: 2726285