The biHecke monoid of a finite Coxeter group - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2010

The biHecke monoid of a finite Coxeter group

Résumé

The usual combinatorial model for the 0-Hecke algebra of the symmetric group is to consider the algebra (or monoid) generated by the bubble sort operators. This construction generalizes to any finite Coxeter group W. The authors previously introduced the Hecke group algebra, constructed as the algebra generated simultaneously by the bubble sort and antisort operators, and described its representation theory. In this paper, we consider instead the monoid generated by these operators. We prove that it has |W| simple and projective modules. In order to construct a combinatorial model for the simple modules, we introduce for each w in W a combinatorial module whose support is the interval [1,w] in right weak order. This module yields an algebra, whose representation theory generalizes that of the Hecke group algebra. This involves the introduction of a w-analogue of the combinatorics of descents of W and a generalization to finite Coxeter groups of blocks of permutation matrices.

Dates et versions

hal-00632270 , version 1 (13-10-2011)
hal-00632270 , version 2 (24-08-2015)

Identifiants

Citer

Florent Hivert, Anne Schilling, Nicolas M. Thiéry. The biHecke monoid of a finite Coxeter group. Discrete Mathematics and Theoretical Computer Science, 2010, 01, pp.dmAN0116. ⟨hal-00632270v1⟩
243 Consultations
569 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More