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## Drinfeld-Gaitsgory-Vinberg interpolation Grassmannian and geometric Satake equivalence

Journal of Topology. 2020. Vol. 13. No. 2. P. 683-729.

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 Gr G . 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.