Quantum cohomology of the Springer resolution
Abstract
Let G denote a complex, semisimple, simplyconnected group. We identify the equivariant quantum differential equation for the cotangent bundle to the flag variety of G with the affine KnizhnikZamolodchikov 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2009
 arXiv:
 arXiv:1001.0056
 Bibcode:
 2010arXiv1001.0056B
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematics  Representation Theory