Open AccessDeligne-Lusztig theoretic derivation for Weyl groups of the number of reflection factorizations of a Coxeter element
Author(s) -
Jean Michel
Publication year - 2015
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc12753
Subject(s) - coxeter group , weyl group , coxeter element , mathematics , character (mathematics) , longest element of a coxeter group , element (criminal law) , coxeter complex , point group , pure mathematics , expression (computer science) , reflection (computer programming) , series (stratigraphy) , product (mathematics) , basis (linear algebra) , algebra over a field , combinatorics , artin group , geometry , computer science , geology , law , programming language , paleontology , political science
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.