14 papers
Lattice structure of Weyl groups via representation theory of preprojective algebras
Osamu Iyama, Nathan Reading, Idun Reiten +1
This paper studies the combinatorics of lattice congruences of the weak order on a finite Weyl group , using representation theory of the corresponding preprojective algebra $Î…
A Cambrian framework for the oriented cycle
Nathan Reading, David E. Speyer
This paper completes the project of constructing combinatorial models (called frameworks) for the exchange graph and g-vector fan associated to any exchange matrix B whose Cartan c…
Combinatorial frameworks for cluster algebras
Nathan Reading, David E Speyer
We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed…
Sortable Elements for Quivers with Cycles
Nathan Reading, David E Speyer
Each Coxeter element c of a Coxeter group W defines a subset of W called the c-sortable elements. The choice of a Coxeter element of W is equivalent to the choice of an acyclic ori…
Noncrossing partitions of a marked surface
Nathan Reading
We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattic…
A combinatorial approach to scattering diagrams
Nathan Reading
Scattering diagrams arose in the context of mirror symmetry, but a special class of scattering diagrams (the cluster scattering diagrams) were recently developed to prove key struc…