Abstract : A Peterson variety is a subvariety of the flag variety $G/B$ defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type A Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives a Chevalley-Monk rule and Giambelli's formula for all Lie types.
https://hal.inria.fr/hal-01207557 Contributor : Coordination Episciences IamConnect in order to contact the contributor Submitted on : Thursday, October 1, 2015 - 9:28:20 AM Last modification on : Tuesday, August 6, 2019 - 11:38:50 AM Long-term archiving on: : Saturday, January 2, 2016 - 10:39:19 AM
Elizabeth Drellich. Chevalley-Monk and Giambelli formulas for Peterson Varieties. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.875-886, ⟨10.46298/dmtcs.2449⟩. ⟨hal-01207557⟩