PIRSA:26030078 Scientific Series Mathematical physics

DOI10.48660/26030078

Series: Mathematical Physics

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}}
}

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.

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