1 citations · 1 across the 8 of their papers we have counts for
8 papers
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…
An introduction to -bands
Luca Francone, Bernard Leclerc
We give an introduction to our results on cluster structures for schemes of -bands emphasizing their connections with seminal works of Frenkel and Reshetikhin in the 90's. I…
Cluster structures on schemes of bands
Luca Francone, Bernard Leclerc
We introduce new objects, called -bands, associated with a simple simply-connected algebraic group , and a Coxeter element in its Weyl group. We show that bands of a…
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…
Generalised spherical minors and their relations
Luca Francone
Let H be a spherical subgroup of minimal rank of the semisimple simply connected complex algebraic group G. We define some functions on the homogeneous space G/H that we call gener…
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…
The minimal monomial lfting of cluster algebras I: branching problems
Luca Francone
Let be complex reductive algebraic groups. The branching problem that aims to study -modules as -modules is encoded by a collection of branc…
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…