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Summary: Positivity in the cohomology of flag bundles (after
Graham)
Dave Anderson
December 15, 2007
In [Gr], Graham proves that the structure constants of the equivariant
cohomology ring of a flag variety are positive combinations of monomials in
the simple roots:
Theorem 1 ([Gr, Cor. 4.1]) Let X = G/B be the flag variety for a com-
plex semisimple group G with maximal torus T B, and let {w H
T X | w
W} be the basis of (B-invariant) Schubert classes. Let {i} be the simple
roots which are negative on B. Then in the expansion
u · v =
w
cw
uv w,
the coefficients cw
uv are in Z0[].
Graham deduces this from a more general result about varieties with finitely
many unipotent orbits, which is proved using induction and a calculation
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