Odd length in Weyl groups

Brenti, Francesco; Carnevale, Angela

doi:10.5802/alco.69

Brenti, Francesco ¹ ; Carnevale, Angela ²

¹ Dipartimento di Matematica Università di Roma “Tor Vergata” Via della Ricerca Scientifica, 1 00133 Roma, Italy
² Fakultät für Mathematik Universität Bielefeld Postfach 100131 D-33501 Bielefeld, Germany

Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1125-1147.

Résumé

We define for any crystallographic root system a new statistic on the corresponding Weyl group which we call the odd length. This statistic reduces, for Weyl groups of types $A$ , $B$ , and $D$ , to the each of the statistics by the same name that have already been defined and studied in [8], [12], [13], and [3]. We show that the sign-twisted generating function of the odd length always factors completely, and we obtain multivariate analogues of these factorizations in types $B$ and $D$ .

Reçu le : 2018-08-19
Révisé le : 2019-02-28
Accepté le : 2019-03-02
Publié le : 2019-12-04

MR Zbl

DOI : 10.5802/alco.69

Classification : 17B22, 20F55, 05E99
Mots clés : Root system, Weyl group, Coxeter group, odd length, enumeration.

Affiliations des auteurs :

Brenti, Francesco ¹ ; Carnevale, Angela ²

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Brenti, Francesco; Carnevale, Angela. Odd length in Weyl groups. Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1125-1147. doi : 10.5802/alco.69. http://www.numdam.org/articles/10.5802/alco.69/

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