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Divided Difference Operator for the Highest root Hessenberg variety

We construct a divided difference operator using GKM theory. This generalizes the classical divided difference operator for the cohomology of the complete flag variety. This construction proves a special case of a recent conjecture of Shareshian and Wachs. Our methods are entirely combinatorial and algebraic, and rely heavily on the combinatorics of root systems and Bruhat order.

preprint2013arXivOpen access
Nicholas Teff
math.COmath.RTmath.AG
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Nicholas Teff

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