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Quantum cohomology of partial flag manifolds and a residue formula for their intersection pairings. (English) Zbl 0849.14019
Under the assumption that the equivariant quantum cohomology of a Kähler manifold is well defined, associative, and a weighted-homogeneous ordinary equivariant $$q$$-deformation of ordinary cohomology, the author computes the equivariant quantum cohomology of partial flag manifolds. The author also derives a general result for some manifolds which present their quantum cohomology as regular functions on complete intersections.

MSC:
 14M15 Grassmannians, Schubert varieties, flag manifolds 57R91 Equivariant algebraic topology of manifolds 81T99 Quantum field theory; related classical field theories 53C55 Global differential geometry of Hermitian and Kählerian manifolds
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