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6 papers · 1 filter
Caldero-Keller approach to the denominators of cluster variables
G. Dupont
Buan, Marsh and Reiten proved that if a cluster-tilting object in a cluster category associated to an acyclic quiver satisfies certain conditions with respect…
From triangulated categories to cluster algebras
Philippe Caldero, Bernhard Keller
The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realize…
Relative Kazhdan--Lusztig cells
Meinolf Geck
In this paper, we study the Kazhdan--Lusztig cells of a Coxeter group in a ``relative'' setting, with respect to a parabolic subgroup . This relies on a factor…
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…
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 …