English

Automata and cells in affine Weyl groups

Group Theory 2008-09-05 v2 Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.0807.2463,
  title  = {Automata and cells in affine Weyl groups},
  author = {Paul E. Gunnells},
  journal= {arXiv preprint arXiv:0807.2463},
  year   = {2008}
}

Comments

fixed typos

R2 v1 2026-06-21T11:00:58.334Z