Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
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作为 Yangian Bethe 代数的旗形余切丛的量子上同调
DOI：
10.1016/j.geomphys.2013.07.006
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发表时间：
2012
影响因子：
1.5
通讯作者：
A. Varchenko
中科院分区：
文献类型：
--
作者：
V. Gorbounov;Richárd Rimányi;V. Tarasov;A. Varchenko
我们将子空间0= F 0的部分标志变量F λ参数化链的余切束的等变上同代数H G L N × C∗（T∗F λ； C）解释为Y (G L N)-模1 D V−的G L N权子空间1 D V λ−的Yangian Bethe代数B∞(1 D V λ−)。在这种识别下，Tarasov and Varchenko(2002)[12]的动态连接转变为Braverman et al.(2010)[4]和Maulik and Okounkov(2012)[5]的量子连接。作为这一鉴定的结果，我们将H G L n× C * * （T * F λ； C）上的量子乘法代数描述为离散Wronski映射的纤维上的函数代数。特别地，它给出了代数的生成器和关系。这种识别也给了我们相关量子微分方程的超几何解。这一事实体现了旗类余切束的朗多-金兹堡镜像对称。
We interpret the equivariant cohomology algebra H G L n× C∗∗(T∗ F λ; C) of the cotangent bundle of a partial flag variety F λ parametrizing chains of subspaces 0= F 0⊂ F 1⊂⋯⊂ F N= C n, dim F i/F i− 1= λ i, as the Yangian Bethe algebra B∞(1 D V λ−) of the g l N-weight subspace 1 D V λ− of a Y (g l N)-module 1 D V−. Under this identification the dynamical connection of Tarasov and Varchenko (2002)[12] turns into the quantum connection of Braverman et al.(2010)[4] and Maulik and Okounkov (2012)[5]. As a result of this identification we describe the algebra of quantum multiplication on H G L n× C∗∗(T∗ F λ; C) as the algebra of functions on fibers of a discrete Wronski map. In particular this gives generators and relations of that algebra. This identification also gives us hypergeometric solutions of the associated quantum differential equation. That fact manifests the Landau–Ginzburg mirror symmetry for the cotangent bundle of the flag variety.
通过恶性步行者和密切步行者的量子上同调
影响因子：
1.2
作者：
Korff C
通讯作者：
Korff C