36 citations · 117 across the 18 of their papers we have counts for
5 papers · 1 filter
Affine cluster monomials are generalized minors
Dylan Rupel, Salvatore Stella, Harold Williams
We study the realization of acyclic cluster algebras as coordinate rings of Coxeter double Bruhat cells in Kac-Moody groups. We prove that all cluster monomials with g-vector lying…
Some Consequences of Categorification
Dylan Rupel, Salvatore Stella
Several conjectures on acyclic skew-symmetrizable cluster algebras are proven as direct consequences of their categorification via valued quivers. These include conjectures of Fomi…
A -Tilting Approach to Dissections of Polygons
Vincent Pilaud, Pierre-Guy Plamondon, Salvatore Stella
We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support -tilting simplicial complex of an explicit finite dimensional alge…
An affine almost positive roots model
Nathan Reading, Salvatore Stella
We generalize the almost positive roots model for cluster algebras from finite type to a uniform finite/affine type model. We define the almost positive Schur roots and a com…
Polytopal realizations of finite type -vector fans
Christophe Hohlweg, Vincent Pilaud, Salvatore Stella
This paper shows the polytopality of any finite type -vector fan, acyclic or not. In fact, for any finite Dynkin type , we construct a universal associahedron $\math…