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A Divided Difference Operator

Abstract : 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.
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https://hal.inria.fr/hal-01229699
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Nicholas Teff. A Divided Difference Operator. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.993-1004. ⟨hal-01229699⟩

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