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

2020/08/21 by Lin Chen, Chen, Lin · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.2008.09349

100 pages; correction of typos

arxiv created 2021/12/18 · arxiv updated 2021/12/21

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.

Citations

• Picard–Lefschetz oscillators for the Drinfeld–Lafforgue–Vinberg degeneration for SL2
• Geometric Bernstein Asymptotics and the Drinfeld-Lafforgue-Vinberg degeneration for arbitrary reductive groups

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