PBW degenerations, quiver Grassmannians, and toric varieties
Evgeny Feigin
HSE University, Faculty of Mathematics, Usacheva 6, Moscow, 119048, Russia, and Skolkovo Institute of Science and Technology, Center for Advanced Studies, Bolshoy Boulevard 30, bld. 1, Moscow 121205, Russia
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Abstract
We present a review on the recently discovered link between the Lie theory, the theory of quiver Grassmannians, and various degenerations of flag varieties. Our starting point is the induced Poincaré–Birkhoff–Witt filtration on the highest weight representations and the corresponding PBW degenerate flag varieties.