q -hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem
q -hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem
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q - 量子微分方程、量子皮耶里规则和伽玛定理的超几何解
DOI：
10.1016/j.geomphys.2019.04.005
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发表时间：
2019
影响因子：
1.5
通讯作者：
Varchenko, Alexander
中科院分区：
文献类型：
--
作者：
Tarasov, Vitaly;Varchenko, Alexander
本文描述了部分旗簇F λ的余切丛T <$F λ的等变量子微分方程和相应的qKZ差分方程的q-超几何解.这些q-超几何解表明余切丛具有Landau-Ginzburg镜像对称性。我们制定和证明的余切丛的量子等变上同调的Pieri规则。我们关于T <$F λ的Gamma定理表明，q-超几何解的渐近性的首项可以写为T <$F λ的切丛的等变Gamma类乘以相关向量丛的等变第一Chern类的指数。这一陈述类似于B关于伽玛猜想的陈述。Dubrovin和S. Galkin，V. Golyshev，and H. Iritani，也见附录B中F λ的Gamma定理。
We describe q-hypergeometric solutions of the equivariant quantum differential equations and the associated qKZ difference equations for the cotangent bundle T∗ F λ of a partial flag variety F λ. These q-hypergeometric solutions manifest a Landau–Ginzburg mirror symmetry for the cotangent bundle. We formulate and prove Pieri rules for quantum equivariant cohomology of the cotangent bundle. Our Gamma theorem for T∗ F λ says that the leading term of the asymptotics of the q-hypergeometric solutions can be written as the equivariant Gamma class of the tangent bundle of T∗ F λ multiplied by the exponentials of the equivariant first Chern classes of the associated vector bundles. That statement is analogous to the statement of the gamma conjecture by B. Dubrovin and by S. Galkin, V. Golyshev, and H. Iritani, see also the Gamma theorem for F λ in Appendix B.