The biHecke monoid of a finite Coxeter group
Identifieur interne : 000A61 ( Main/Exploration ); précédent : 000A60; suivant : 000A62The biHecke monoid of a finite Coxeter group
Auteurs : Florent Hivert [France] ; Anne Schilling [États-Unis] ; Nicolas M. Thiéry [France]Source :
English descriptors
Abstract
For any finite Coxeter group W, we introduce two new objects: its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W. The construction of the biHecke monoid relies on the usual combinatorial model for the 0-Hecke algebra H_0(W), that is, for the symmetric group, the algebra (or monoid) generated by the elementary bubble sort operators. 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 \emphmonoid generated by these operators. We prove that it admits |W| simple and projective modules. In order to construct the simple modules, we introduce for each w∈W a combinatorial module T_w whose support is the interval [1,w]_R in right weak order. This module yields an algebra, whose representation theory generalizes that of the Hecke group algebra, with the combinatorics of descents replaced by that of blocks and of the cutting poset. \par
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Affiliations:
- France, États-Unis
- Haute-Normandie, Région Normandie
- Le Havre, Rouen
- Université de Rouen, Université du Havre
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The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W. The construction of the biHecke monoid relies on the usual combinatorial model for the 0-Hecke algebra H_0(W), that is, for the symmetric group, the algebra (or monoid) generated by the elementary bubble sort operators. 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 \emphmonoid generated by these operators. We prove that it admits |W| simple and projective modules. In order to construct the simple modules, we introduce for each w∈W a combinatorial module T_w whose support is the interval [1,w]_R in right weak order. This module yields an algebra, whose representation theory generalizes that of the Hecke group algebra, with the combinatorics of descents replaced by that of blocks and of the cutting poset. \par</div></front></TEI><affiliations><list><country><li>France</li><li>États-Unis</li></country><region><li>Haute-Normandie</li><li>Région Normandie</li></region><settlement><li>Le Havre</li><li>Rouen</li></settlement><orgName><li>Université de Rouen</li><li>Université du Havre</li></orgName></list><tree><country name="France"><region name="Région Normandie"><name sortKey="Hivert, Florent" sort="Hivert, Florent" uniqKey="Hivert F" first="Florent" last="Hivert">Florent Hivert</name></region><name sortKey="Thiery, Nicolas M" sort="Thiery, Nicolas M" uniqKey="Thiery N" first="Nicolas M." last="Thiéry">Nicolas M. Thiéry</name></country><country name="États-Unis"><noRegion><name sortKey="Schilling, Anne" sort="Schilling, Anne" uniqKey="Schilling A" first="Anne" last="Schilling">Anne Schilling</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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