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Quantum cohomology of partial flag manifoldsF_{n_1 } \ldots _{n_k }

Authors:	Alexander Astashkevich Vladimir Sadov

Institution:	(1) Department of Mathematics, M.I.T., 02139 Cambridge, MA, USA;(2) Lyman Laboratory of Physics, Harvard University, 02138 Cambridge, MA, USA;(3) L.D. Landau Institute for Theoretical Physics, Moscow, Russia

Abstract:	We compute the quantum cohomology rings of the partial flag manifolds $F_{n_1 } \ldots _{n_k } = U(n)/(U(n_1 ) \times \cdots \times U(n_k ))$ . The inductive computation uses the idea of Givental and Kim 1]. Also we define a notion of the vertical quantum cohomology ring of the algebraic bundle. For the flag bundle $F_{n_1 } \ldots _{n_k }$ (E) associated with the vector bundleE this ring is found.

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