PIRSA:25050010 Scientific Series Mathematical physics

DOI10.48660/25050010

Series: Mathematical Physics

Dumanskiy, I. (2025). Perverse coherent sheaves and cluster categorifications. Perimeter Institute. https://pirsa.org/25050010

Dumanskiy, Ilya. Perverse coherent sheaves and cluster categorifications. Perimeter Institute, May. 08, 2025, https://pirsa.org/25050010 

@misc{ pirsa_PIRSA:25050010,
  doi = {10.48660/25050010},
  url = {https://pirsa.org/25050010},
  author = {Dumanskiy, Ilya},
  keywords = {Mathematical physics},
  language = {en},
  title = {Perverse coherent sheaves and cluster categorifications},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {may},
  note = {PIRSA:25050010 see, \url{https://pirsa.org}}
}

Abstract

K-theoretical Coulomb branches are expected to have cluster structure. Cautis and Williams categorified this expectation. In particular, they conjecture (and prove in type A) that the category of perverse coherent sheaves on the affine Grassmannian is a cluster monoidal categorification. We discuss recent progress on this conjecture. In particular, we construct cluster short exact sequences of certain perverse coherent sheaves. We do that by constructing a bridge, relating this (geometric) category to the (algebraic) category of finite dimensional modules over the quantum affine group. This is done by relating both categories to the notion of Feigin--Loktev fusion product.

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