# Quantization of Drinfeld Zastava in type $A$

Michael Finkelberg; Leonid Rybnikov

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 2, page 235-271
- ISSN: 1435-9855

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topFinkelberg, Michael, and Rybnikov, Leonid. "Quantization of Drinfeld Zastava in type $A$." Journal of the European Mathematical Society 016.2 (2014): 235-271. <http://eudml.org/doc/277663>.

@article{Finkelberg2014,

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 $\widehat\{\mathfrak \{sl\}\}_n$. 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.},

author = {Finkelberg, Michael, Rybnikov, Leonid},

journal = {Journal of the European Mathematical Society},

keywords = {$q$-difference Toda lattice; equivariant $K$-theory; Laumon compactification; Drinfeld Zastava; moduli space; projective line; Kashiwara flag scheme; Lie algebra; quiver variety; Poisson structure; Hamiltonian reduction; Drinfeld Zastava; moduli space; projective line; Kashiwara flag scheme; Lie algebra; quiver variety; Poisson structure; Hamiltonian reduction; quantization; Yangian},

language = {eng},

number = {2},

pages = {235-271},

publisher = {European Mathematical Society Publishing House},

title = {Quantization of Drinfeld Zastava in type $A$},

url = {http://eudml.org/doc/277663},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Finkelberg, Michael

AU - Rybnikov, Leonid

TI - Quantization of Drinfeld Zastava in type $A$

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 2

SP - 235

EP - 271

AB - 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 $\widehat{\mathfrak {sl}}_n$. 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.

LA - eng

KW - $q$-difference Toda lattice; equivariant $K$-theory; Laumon compactification; Drinfeld Zastava; moduli space; projective line; Kashiwara flag scheme; Lie algebra; quiver variety; Poisson structure; Hamiltonian reduction; Drinfeld Zastava; moduli space; projective line; Kashiwara flag scheme; Lie algebra; quiver variety; Poisson structure; Hamiltonian reduction; quantization; Yangian

UR - http://eudml.org/doc/277663

ER -

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