Quantization of Drinfeld Zastava in type $A$

Finkelberg, 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 -