论文标题
在Drinfeld-Gaitsgory-Vinberg插值司法和长互穿函数的附近周期
Nearby cycles on Drinfeld-Gaitsgory-Vinberg Interpolation Grassmannian and long intertwining functor
论文作者
论文摘要
令$ g $为一个还原组，$ u，u^ - $是一对抛物线子群体的一项单位激进分子$ p，p^ - $。我们证明$ u（\！（t）\！）$ - epivariant和$ u^ - （\！（t）\！）$ - equivariant d-modules的dg类别是彼此规定的。我们表明，目睹这种二元性的单位对象是由Drinfeld-Gaitsgory-Vinberg插值Grassmannian在Arxiv中定义的：1805.07721中给出的。我们研究了附近周期的各种特性，特别是将它们与Arxiv中研究的附近周期相提并论：1411.4206和ARXIV：1607.00586。我们还将结果推广到Beilinson-Drinfeld Grassmannian $ gr_ {g，X^i} $，并将其仿射标志品种$ fl_g $。
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 $Fl_G$.
