Assuming the Ben-Zvi-Sakellaridis-Venkatesh local conjecture and polarization, the authors deduce a Z/2-graded equivalence between B-equivariant D-modules on Y and unipotent B^vee-monodromic modules on the dual variety via S1-equivariant localization.
Knop, On the set of orbits for a Borel subgroup , Comment.\ Math.\ Helvetici 70 (1995), 285--309
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Relative Langlands duality and Koszul duality
Assuming the Ben-Zvi-Sakellaridis-Venkatesh local conjecture and polarization, the authors deduce a Z/2-graded equivalence between B-equivariant D-modules on Y and unipotent B^vee-monodromic modules on the dual variety via S1-equivariant localization.