Equivariant Cohomology of Laumon's Quasiflags Spaces and the Quantum Calogero-Moser Hamiltonian
| SPECIAL LECTURE | |
| Topic: | Equivariant Cohomology of Laumon's Quasiflags Spaces and the Quantum Calogero-Moser Hamiltonian |
| Speaker: | Andrei Negut |
| Affiliation: | Princeton University |
| Date: | Thursday, May 1 |
| Time/Room: | 2:00pm - 3:30pm/S-101 |
We will introduce certain operators A(m) on the equivariant cohomology ring of the Laumon quasiflags spaces M_d . The character of A(m) will be equal to the generating function Z(m) of the integrals of the Chern polynomial of the tangent bundle of the spaces M_d . We will study certain factorizations of A(m) , and interpret these factorizations both geometrically and representation-theoretically. The representation theoretic interpretation will allow us to show that the character Z(m) is (up to a constant monomial) the Jack polynomial, and thus very closely related to the universal eigenfunction of the quantum Calogero-Moser hamiltonian. Joint work with Andrei Okounkov.