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Polynomiality of the equivariant Euler characteristic of a sheaf tensored with a standard line bundle on the flag variety

Let ${\mathcal B}=Fl(V)$ be the variety of complete flags in an $(m+2n)$-dimensional vector space $V$ over $\mathbb C$. Then we have the standard line bundles $\mathcal{O}(\lambda)$ on $\mathcal B$ ...
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