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Fano compactifications of mutation algebras
Joshua Enwright, Luca Francone, Joaquín Moraga +1
In this article, we introduce the notion of mutation semigroup algebras. This concept simultaneously generalizes cluster algebras and semigroup algebras. We show that, under some m…
Cluster structures on Cox rings
Luca Francone
We construct a graded cluster algebra structure on the Cox ring of a smooth complex variety , depending on a base cluster structure on the ring of regular functions of an open s…
Intersection multiplicity one for the Belkale-Kumar product in G/B
Nicolas Ressayre, Luca Francone
Consider the complete flag variety of a complex semisimple algebraic group . We show that the structure coefficients of the Belkale-Kumar product , on the cohomolog…
On the multiplicity spaces for branching to a spherical subgroup of minimal rank
Luca Francone, Nicolas Ressayre
Let g be a complex semi-simple Lie algebra and g be a semisimple subalgebra of g. Consider the branching problem of decomposing the simple g-representations V as a sum of simple gr…