Geodesic
Monk's rule and Giambelli's formula for Peterson varieties of all Lie types
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 2, pp. 539-575.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

A Peterson variety is a subvariety of the flag variety $G/B$ which appears in the construction of the quantum cohomology of partial flag varieties. 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 (arXiv:0908.3517, 2009), and Bayegan-Harada gave Giambelli's formula (arXiv:1012.4053, 2010) for multiplication in the cohomology ring. This paper gives Monk's rule and Giambelli's formula for all Lie types.
Classification : 14N15, 55N91, 14M15
Keywords: Peterson variety, equivariant cohomology, Monk's rule, Giambelli's formula, Schubert calculus 
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     title = {Monk's rule and {Giambelli's} formula for {Peterson} varieties of all {Lie} types},
     journal = {Journal of Algebraic Combinatorics},
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Drellich, Elizabeth. Monk's rule and Giambelli's formula for Peterson varieties of all Lie types. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 2, pp. 539-575. http://geodesic.mathdoc.fr/item/JAC_2015__41_2_a1/