Nearby cycles on Drinfeld–Gaitsgory–Vinberg interpolation Grassmannian and long intertwining functor

Let G be a reductive group, and let U, U− the unipotent radicals of pair opposite parabolic subgroups P, P−. We prove that DG categories U((t))-equivariant U−((t))-equivariant D-modules on affine Grassmannian GrG are canonically dual to each other. show unit object witnessing this duality is given by nearby cycles Drinfeld–Gaitsgory–Vinberg interpolation defined in recent work Finkelberg, Krylov, Mirković. study various properties mentioned cycles, particular compare them with studied works Schieder. also generalize our results Beilinson–Drinfeld GrG,XI flag variety FlG. This version paper contains fewer appendices than submitted arXiv.