Special Seminar

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.