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Working paper

Drinfeld-Gaitsgory interpolation Grassmannian and geometric Satake equivalence (with appendix by Dennis Gaitsgory)

Let G be a reductive complex algebraic group. We fix a pair of opposite Borel subgroups and consider the corresponding semiinfinite 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 semiinfinite orbits with U(𝔫ˇ) (the universal enveloping algebra of the positive nilpotent subalgebra of the Langlands dual Lie algebra 𝔤ˇ). 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.