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5 papers · 1 filter
Kazhdan--Lusztig cells and the Murphy basis
Meinolf Geck
Let be the Iwahori--Hecke algebra associated with , the symmetric group on symbols. This algebra has two important bases: the Kazhdan--Lusztig basis and the Murphy bas…
Quivers with relations and cluster tilted algebras
Philippe Caldero, Frederic Chapoton, Ralf Schiffler
Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. To a cluster algebra of simply laced Dynkin type one can associate the clust…
Sur le nombre de reflexions pleines dans les groupes de Coxeter finis
Frederic Chapoton
On etudie divers aspects d'une formule qui compte les reflexions pleines dans les groupes de Coxeter finis. ***** We study several points about a formula which counts reflexions in…
Left cells and constructible representations
Meinolf Geck
We consider the partition of a finite Coxeter group into left cells with respect to a weight function . In the equal parameter case, Lusztig has shown that the representatio…
Computing Kazhdan--Lusztig cells for unequal parameters
Meinolf Geck
Following Lusztig, we consider a Coxeter group together with a weight function . This gives rise to the pre-order relation and the corresponding partition of …