JournalsjemsVol. 16, No. 2pp. 235–271

Quantization of Drinfeld Zastava in type AA

  • Michael Finkelberg

    Independent University of Moscow, Russian Federation
  • Leonid Rybnikov

    Independent University of Moscow, Russian Federation
Quantization of Drinfeld Zastava in type $A$ cover
Download PDF

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\hat{sl}_n. We introduce an affine, reduced, irreducible, normal quiver variety ZZ 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 ZZ 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 YY of the coordinate ring of ZZ. 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, YY is a quotient of the affine Borel Yangian.

Cite this article

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

DOI 10.4171/JEMS/432