Eduardo Gonzalez:Nil-Hecke algebras and Quantum Cohomology

Abstract: Let $M$ be a (monotone) symplectic manifold endowed with a Hamiltonian action of a compact Lie group $G$ with maximal torus $T$. We construct an action of the cohomology of the affine flag manifold $LG/T$ onto the quantum cohomology of $M$. Our construction generalises that of Okounkov et. all of shift operators and Seidel's representation. This is joint work with Cheuk Yu Mak and Dan Pomerleano.