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.
https://hal.inria.fr/hal-01229699 Contributor : Alain MonteilConnect in order to contact the contributor Submitted on : Tuesday, November 17, 2015 - 10:20:09 AM Last modification on : Tuesday, March 7, 2017 - 3:23:59 PM Long-term archiving on: : Thursday, February 18, 2016 - 11:41:18 AM
Nicholas Teff. A Divided Difference Operator. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.993-1004, ⟨10.46298/dmtcs.2360⟩. ⟨hal-01229699⟩