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arXiv · 2008.09349

Nearby cycles on Drinfeld-Gaitsgory-Vinberg Interpolation Grassmannian and long intertwining functor

Lin Chen
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Abstract

Let $G$ be a reductive group and $U,U^-$ be the unipotent radicals of a pair of opposite parabolic subgroups $P,P^-$. We prove that the DG-categories of $U(\!(t)\!)$-equivariant and $U^-(\!(t)\!)$-equivariant D-modules on the affine Grassmannian $Gr_G$ are canonically dual to each other. We show that the unit object witnessing this duality is given by nearby cycles on the Drinfeld-Gaitsgory-Vinberg interpolation Grassmannian defined in arXiv:1805.07721. We study various properties of the mentioned nearby cycles, in particular compare them with the nearby cycles studied in arXiv:1411.4206 and arXiv:1607.00586. We also generalize our results to the Beilinson-Drinfeld Grassmannian $Gr_{G,X^I}$ and to the affine flag variety $Fl_G$.

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Lin Chen. 2020-08-21. Nearby cycles on Drinfeld-Gaitsgory-Vinberg Interpolation Grassmannian and long intertwining functor. https://arxiv.org/abs/2008.09349

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