Quantum cohomology of partial flag manifolds
Abstract
We compute the quantum cohomology rings of the partial flag manifolds Fn1·s nk=U(n)/(U(n1)× ·s × U(nk)). The inductive computation uses the idea of Givental and Kim. Also we define a notion of the vertical quantum cohomology ring of the algebraic bundle. For the flag bundle Fn1·s nk(E) associated with the vector bundle E this ring is found.
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