A positive formula for type a Peterson Schubert calculus

DOI10.1007/s44007-022-00023-0OpenAlexW3015872364WikidataQ113890323 ScholiaQ113890323MaRDI QIDQ2674975

Brent Gorbutt, Rebecca Goldin

Publication date: 19 September 2022

Published in: La Matematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.05959

zbMATH Keywords

Schubert calculusVandermondestructure constantsPeterson

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Classical problems, Schubert calculus (14N15)

Related Items

Remixed Eulerian numbers ⋮ Toward cohomology rings of intersections of Peterson varieties and Richardson varieties

Cites Work

• Unnamed Item
• The equivariant cohomology rings of Peterson varieties
• Hessenberg varieties and hyperplane arrangements
• Common origin of cubic binomial identities: A generalization of Surányi's proof on Le Jen Shoo's formula
• Equivariant cohomology, Koszul duality, and the localization theorem
• Positivity in equivariant Schubert calculus.
• The equivariant cohomology ring of regular varieties
• Flag manifold quantum cohomology, the Toda lattice, and the representation with highest weight \(\rho\)
• Kostant polynomials and the cohomology ring for \(G/B\)
• Monk's rule and Giambelli's formula for Peterson varieties of all Lie types
• Paving Hessenberg varieties by affines
• A mirror symmetric construction of \(qH_T^*(G/P)_{(q)}\)
• Topological Schur lemma and related results
• Intersection theory of the Peterson variety and certain singularities of Schubert varieties
• A positive Monk formula in the S ¹ -equivariant cohomology of type A Peterson varieties
• Totally positive Toeplitz matrices and quantum cohomology of partial flag varieties
• The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types
• Poincaré duality and equivariant (co)homology.