77 citations · 179 across the 13 of their papers we have counts for
6 papers · 1 filter
Differential operators on the base affine space of and quantized Coulomb branches
Tom Gannon, Harold Williams
We show that the algebra of differential operators on the base affine space of is the quantized Coulomb branch of a certain 3d quiver gau…
Cluster theory of the coherent Satake category
Sabin Cautis, Harold Williams
We study the category of G(O)-equivariant perverse coherent sheaves on the affine Grassmannian of G. This coherent Satake category is not semisimple and its convolution product is…
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…
On Generalized Minors and Quiver Representations
Dylan Rupel, Salvatore Stella, Harold Williams
The cluster algebra of any acyclic quiver can be realized as the coordinate ring of a subvariety of a Kac-Moody group -- the quiver is an orientation of its Dynkin diagram, definin…
Toda Systems, Cluster Characters, and Spectral Networks
Harold Williams
We show that the Hamiltonians of the open relativistic Toda system are elements of the generic basis of a cluster algebra, and in particular are cluster characters of nonrigid repr…
Q-Systems, Factorization Dynamics, and the Twist Automorphism
Harold Williams
We provide a concrete realization of the cluster algebras associated with Q-systems as amalgamations of cluster structures on double Bruhat cells in simple algebraic groups. For no…