Chi Hong Chow - Peterson/Lam-Shimozono's theorem via Seidel representations

October 8, 12 pm ET: Chi Hong Chow (CUHK) - Peterson/Lam-Shimozono's theorem via Seidel representations

Abstract: I will present a new proof of a theorem of Peterson and Lam-Shimozono which gives an explicit ring homomorphism from the based loop homology of a compact semi-simple Lie group to the quantum cohomology of any of its coadjoint orbits. This map is in general surjective after localization with explicit kernel and bijective when the coadjoint orbit has maximal dimension. The idea is to compute Savelyev's parametrized version of Seidel representations. Surprisingly, it turns out to be equal to the map of Peterson and Lam-Shimozono. I will also discuss some applications to the Hamiltonian groups of coadjoint orbits.