Monk's rule and Giambelli's formula for Peterson varieties of all Lie types

DOI10.1007/s10801-014-0545-2zbMath1338.14051arXiv1311.3014OpenAlexW3102231091MaRDI QIDQ2264037

Elizabeth Drellich

Publication date: 20 March 2015

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.3014

zbMATH Keywords

Schubert calculusequivariant cohomologyGiambelli's formulaMonk's rulePeterson variety

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Equivariant homology and cohomology in algebraic topology (55N91) Classical problems, Schubert calculus (14N15)

Related Items

A positive formula for type a Peterson Schubert calculus ⋮ The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials ⋮ Toward cohomology rings of intersections of Peterson varieties and Richardson varieties ⋮ A Survey of Recent Developments on Hessenberg Varieties ⋮ The singular locus of semisimple Hessenberg varieties ⋮ The Containment Poset of Type $A$ Hessenberg Varieties ⋮ A formula for the cohomology and \(K\)-class of a regular Hessenberg variety ⋮ An equivariant basis for the cohomology of Springer fibers

Cites Work

• Unnamed Item
• Equivariant cohomology, Koszul duality, and the localization theorem
• Flag manifold quantum cohomology, the Toda lattice, and the representation with highest weight \(\rho\)
• Patch ideals and Peterson varieties
• A Giambelli formula for the \(S^1\)-equivariant cohomology of type \(A\) Peterson varieties
• Kostant polynomials and the cohomology ring for \(G/B\)
• Poset pinball, GKM-compatible subspaces, and Hessenberg varieties
• A Gröbner basis for Kazhdan-Lusztig ideals
• A positive Monk formula in the S ¹ -equivariant cohomology of type A Peterson varieties
• Combinatorics of Coxeter Groups
• Excited Young diagrams and equivariant Schubert calculus
• A Mirror Construction for the Totally Nonnegative Part of the Peterson Variety