Equivariant quantum cohomology and the geometric Satake equivalence
Massachusetts Institute of Technology. Department of Mathematics.
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Recent work on equivariant aspects of mirror symmetry has discovered relations between the equivariant quantum cohomology of symplectic resolutions and Casimir-type connections (among many other objects). We provide a new example of this theory in the setting of the affine Grassmannian, a fundamental space in the geometric Langlands program. More precisely, we identify the equivariant quantum connection of certain symplectic resolutions of slices in the affine Grassmannian of a semisimple group G with a trigonometric Knizhnik-Zamolodchikov (KZ)-type connection of the Langlands dual group of G. These symplectic resolutions are expected to be symplectic duals of Nakajima quiver varieties, and thus our result is an analogue of (part of) the work of Maulik and Okounkov in the symplectic dual setting.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 41-45).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.; Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology