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Consider a sum of m copies of the tautological bundle over the Grassmannian of n-planes in complex k-dimensional vector space. There is an obvious action of an (m+k)-dimensional torus T on the total space of this bundle. Did anybody compute the T-equivariant quantum cohomology ring of this space? Or perhaps T-equivariant quantum K-theory?

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The center of $GL_k$ acts in the same way as the diagonal in the $m$-dimensional torus. So, your action has 1-dimensional kernel. – Sasha Sep 15 '12 at 15:10
    
(Oops, I had a wrong comment based on misreading $k$ vs. $n$ -- the literature I read all has $k$-planes in $n$-space, not the reverse.) – Allen Knutson Sep 18 '12 at 10:05

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