Quantization of Drinfeld zastava in type C

A 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 ĝ. In case g is the symplectic Lie algebra sp_N, 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 the 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 the work of Gerasimov-Kharchev-Lebedev-Oblezin (2005). We prove that Y is a quotient of the affine Borel Yangian. The analogous results for g = sl_N were obtained in our previous work.