Quantum cohomology of the Springer resolution
Algebraic Geometry
2010-09-07 v2 High Energy Physics - Theory
Representation Theory
Abstract
Let G denote a complex, semisimple, simply-connected group. We identify the equivariant quantum differential equation for the cotangent bundle to the flag variety of G with the affine Knizhnik-Zamolodchikov connection of Cherednik and Matsuo. This recovers Kim's description of quantum cohomology of the flag variety itself as a limiting case. A parallel result is proven for resolutions of the Slodowy slices. Extension to arbitrary symplectic resolutions is discussed.
Keywords
Cite
@article{arxiv.1001.0056,
title = {Quantum cohomology of the Springer resolution},
author = {Alexander Braverman and Davesh Maulik and Andrei Okounkov},
journal= {arXiv preprint arXiv:1001.0056},
year = {2010}
}