Quantization of Drinfeld zastava in type C

Michael Finkelberg, Leonid Rybnikov

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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 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 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 = slN were obtained in our previous work.

Original languageEnglish
Pages (from-to)166-180
Number of pages15
JournalAlgebraic Geometry
Volume1
Issue number2
DOIs
Publication statusPublished - 1 Mar 2014
Externally publishedYes

Keywords

  • Affine Yangian
  • Chainsaw quiver
  • Hamiltonian reduction
  • Quadratic spaces
  • Quantization

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