Deligne-Lusztig theoretic derivation for Weyl groups of the number of reflection factorizations of a Coxeter element
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Abstract:
Chapuy and Stump have given a nice generating series for the number of factorizations of a Coxeter element as a product of reflections. Their method is to evaluate case by case a character-theoretic expression. The goal of this note is to give a uniform evaluation of their character-theoretic expression in the case of Weyl groups, by using combinatorial properties of Deligne-Lusztig representations.References
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Additional Information
- Jean Michel
- Affiliation: Institut de Mathématiques de Jussieu – Paris rive gauche, Université Denis Diderot, Bâtiment Sophie Germain, 75013, Paris, France
- MR Author ID: 189248
- Received by editor(s): October 13, 2014
- Received by editor(s) in revised form: February 5, 2015
- Published electronically: June 30, 2015
- Communicated by: Pham Huu Tiep
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 937-941
- MSC (2010): Primary 20F55, 5E10
- DOI: https://doi.org/10.1090/proc12753
- MathSciNet review: 3447647