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10 papers · 1 filter
An algorithm for computing the canonical bases of higher-level q-deformed Fock spaces
Xavier Yvonne
We derive a straightening-free algorithm that computes the canonical bases of any higher-level q-deformed Fock space.
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…
Positivity results for the Hecke algebras of non-crystallographic finite Coxeter groups
Fokko Du Cloux
This paper is a report on a computer check of some positivity properties of the Hecke algebra in type H4, including the non-negativity of the coefficients of the structure constant…
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…
Geometric lifting of the canonical basis and semitoric degenerations of Richardson varieties
Sophie Morier-Genoud
In the sl\_n case, A. Berenstein and A. Zelevinsky studied the Schützenberger involution in terms of Lusztig's canonical basis, [3]. We generalize their construction and formulas f…