Quantization of Drinfeld Zastava in type A
Quantization of Drinfeld Zastava in type A
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A 型 Drinfeld Zastava 的量化
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
L. Rybnikov
中科院分区：
文献类型：
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作者：
M. Finkelberg;L. Rybnikov
Drinfeld Zastava是仿射李代数$\hat{sl}_n$的从射影线到Kashiwara旗方案的映射的模空间的某种闭包。我们引入一个仿射，减少，不可约，正常的Zastava品种$Z$映射到Zastava空间双射在复杂的点的水平。Zastava空间上的自然泊松结构可以用（非半单）李代数的对偶空间的某个泊松子簇的Hamilton约化来描述。量子哈密顿约化对应的商的通用包络代数产生量子化$Y $的坐标环$Z $。在arXiv：math/0409031中，在有限（与仿射相反）情况下获得了相同的量化。我们证明，对于通用值的量化参数，$Y$是一个商的仿射Borel杨。
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 $\hat{sl}_n$. 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 arXiv:math/0409031. We prove that, for generic values of quantization parameters, $Y$ is a quotient of the affine Borel Yangian.