Deligne-Lusztig theoretic derivation for Weyl groups of the number of reflection factorizations of a Coxeter element | Zendy

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Deligne-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.

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