Quantization of Drinfeld Zastava in type C

الأصل · EN

Drinfeld zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of an affine Lie algebra g. In case g is the symplectic Lie algebra spₙ, we introduce an affine, reduced, irreducible, normal quiver variety Z which maps to the zastava space isomorphically in characteristic 0. The natural Poisson structure on the zastava space Z can be described in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian reduction of the corresponding quotient of its universal enveloping algebra produces a quantization Y of the coordinate ring of Z. The same quantization was obtained in the finite (as opposed to the affine) case generically in arXiv:math/0409031. We prove that Y is a quotient of the affine Borel Yangian. The analogous results for g=slₙ were obtained in our previous work arXiv:1009.0676.