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Quantization of Drinfeld Zastava in type A

Michael Finkelberg, Leonid Rybnikov (2014)

Journal of the European Mathematical Society

Drinfeld Zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of the affine Lie algebra 𝔰𝔩 ^ n . We introduce an affine, reduced, irreducible, normal quiver variety Z which maps to the Zastava space bijectively at the level of complex points. The natural Poisson structure on the Zastava space can be described on Z in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian...

Quotients of an affine variety by an action of a torus

Olga Chuvashova, Nikolay Pechenkin (2013)

Open Mathematics

Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/C T and the toric Hilbert scheme H. We introduce a notion of the main component H 0 of H, which parameterizes general T-orbit closures in X and their flat limits. The main component U 0 of the universal family U over H is a preimage of H 0. We define an analogue of a universal family WX over the main component of X/C T. We show that the toric Chow morphism restricted on the main components...

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