# Quantization of Drinfeld Zastava in type $A$

### Michael Finkelberg

Independent University of Moscow, Russian Federation### Leonid Rybnikov

Independent University of Moscow, Russian Federation

## Abstract

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 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 [4]. We prove that, for generic values of quantization parameters, $Y$ is a quotient of the affine Borel Yangian.

## Cite this article

Michael Finkelberg, Leonid Rybnikov, Quantization of Drinfeld Zastava in type $A$. J. Eur. Math. Soc. 16 (2014), no. 2, pp. 235–271

DOI 10.4171/JEMS/432