2017/10/09 by Vitaly Tarasov, Tarasov, Vitaly, Alexander Varchenko +1 · 1 citation
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1710.03177
We describe ,q-hypergeometric solutions of the equivariant quantum\ndifferential equations and associated qKZ difference equations for the\ncotangent bundle T^*F_\λ of a partial flag variety ,F_\λ ,.\nThese ,q-hypergeometric solutions manifest a Landau-Ginzburg mirror symmetry\nfor the cotangent bundle. We formulate and prove Pieri rules for quantum\nequivariant cohomology of the cotangent bundle. Our Gamma theorem for\n ,T^*F_\λ ,says that the leading term of the asymptotics of the\n ,q-hypergeometric solutions can be written as the equivariant Gamma class of\nthe tangent bundle of T^*F_\λ multiplied by the exponentials of the\nequivariant first Chern classes of the associated vector bundles. That\nstatement is analogous to the statement of the gamma conjecture by B. ,Dubrovin\nand by S. ,Galkin, V. ,Golyshev, and H. ,Iritani, see also the Gamma theorem\nfor ,F_\λ ,in Appendix B.\n