Drinfeld–Gaitsgory–Vinberg interpolation Grassmannian and geometric Satake equivalence

Michael Finkelberg, Vasily Krylov, Ivan Mirković

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1 Citation (Scopus)

Abstract

Let G be a reductive complex algebraic group. We fix a pair of opposite Borel subgroups and consider the corresponding semi-infinite orbits in the affine Grassmannian GrG. We prove Simon Schieder's conjecture identifying his bialgebra formed by the top compactly supported cohomology of the intersections of opposite semi-infinite orbits with U(n) (the universal enveloping algebra of the positive nilpotent subalgebra of the Langlands dual Lie algebra g). To this end we construct an action of Schieder bialgebra on the geometric Satake fiber functor. We propose a conjectural construction of Schieder bialgebra for an arbitrary symmetric Kac–Moody Lie algebra in terms of Coulomb branch of the corresponding quiver gauge theory.

Original languageEnglish
Pages (from-to)683-729
Number of pages47
JournalJournal of Topology
Volume13
Issue number2
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • 14D24 (secondary)
  • 14M15 (primary)

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