PIRSA:26030078

Cluster Structures for K-theoretic Coulomb Branches of Quiver Theories via Residues

Schrader, G. (2026). Cluster Structures for K-theoretic Coulomb Branches of Quiver Theories via Residues. Perimeter Institute. https://pirsa.org/26030078

Schrader, Gus. Cluster Structures for K-theoretic Coulomb Branches of Quiver Theories via Residues. Perimeter Institute, Mar. 13, 2026, https://pirsa.org/26030078 

          @misc{ pirsa_PIRSA:26030078,
            doi = {10.48660/26030078},
            url = {https://pirsa.org/26030078},
            author = {Schrader, Gus},
            keywords = {Mathematical physics},
            language = {en},
            title = {Cluster Structures for K-theoretic Coulomb Branches of Quiver Theories via Residues},
            publisher = {Perimeter Institute},
            year = {2026},
            month = {mar},
            note = {PIRSA:26030078 see, \url{https://pirsa.org}}
          }

Gus Schrader University of California, Berkeley

Talk numberPIRSA:26030078
DOI10.48660/26030078
Collection
Talk Type Scientific Series
Subject

Abstract

I will explain a recent joint work with A. Shapiro in which we prove that the quantized K-theoretic BFN Coulomb branch ring associated to a quiver gauge theory is isomorphic to a quantum upper cluster algebra, when the gauge theory quiver is without 1-cycles. The new ingredient needed to upgrade our earlier partial results in this direction is a precise description of the image of the Coulomb ring for gauge group G inside the localized equivariant K-theory of the affine Grassmannian Gr_T, where T \subset G is the maximal torus. This description combines conditions on residues at possible simple poles at shifted root hyperplanes with divisibility conditions controlled by the representation N determining the matter content of the theory.