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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.
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…
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…
Cluster algebras as Hall algebras of quiver representations
Philippe Caldero, Frederic Chapoton
Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type…