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 $U({\mathfrak{n}}^{\vee })$ (the universal enveloping algebra of the positive nilpotent subalgebra of the Langlands dual Lie algebra ${\mathfrak{g}}^{\vee }$). 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.

中文翻译：

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Drinfeld–Gaitsgory–Vinberg插值草曼和几何Satake等价

让 $G$是一个还原复数代数群。我们修复一对相对的Borel子群，并考虑仿射Grassmannian中相应的半无限轨道${GR}_G$。我们证明西蒙·席德（Simon Schieder）的猜想可以识别他的双代数，该双代数是由相对半无限轨道与$ü（{\mathfrak{ñ}}^{\vee }）$ （Langlands对偶李代数的正幂等子代数的通用包络代数 ${\mathfrak{G}}^{\vee }$）。为此，我们构造了Schieder双代数对几何Satake纤维函子的作用。我们提出了一个任意对称Kac-Moody Lie代数的Schieder双代数的猜想构造，它是基于相应颤动规理论的库仑分支。