Operator calculus for \(\widetilde{Q}\)-polynomials and Schubert polynomials

DOI10.1006/aima.1998.1757zbMath0951.14035OpenAlexW2072404880MaRDI QIDQ1275428

Piotr Pragacz, Lascoux, Alain

Publication date: 31 May 1999

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.1998.1757

zbMATH Keywords

Schubert polynomialsGiambelli-type formulaLagrangian degeneracy lociLagrangian flag manifolds

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Determinantal varieties (14M12) Grassmannians, Schubert varieties, flag manifolds (14M15) Enumerative problems (combinatorial problems) in algebraic geometry (14N10)

Related Items

Quantum multiplication operators for Lagrangian and orthogonal Grassmannians, Quantum cohomology rings of Lagrangian and orthogonal Grassmannians and total positivity, The Cartan matrix and enumerative calculus, VAFA-INTRILIGATOR TYPE FORMULAS AND QUANTUM EULER CLASSES FOR LAGRANGIAN AND ORTHOGONAL GRASSMANNIANNS, A Giambelli formula for classical 𝐺/𝑃 spaces, Quantum cohomology of the Lagrangian Grassmannian, Galkin's Lower bound Conjecure for Lagrangian and orthogonal Grassmannians, Schubert polynomials, theta and eta polynomials, and Weyl group invariants, Chern class formulas for $G_{2}$ Schubert loci, ALGORITHM FOR MULTIPLYING SCHUBERT CLASSES, Double Schubert polynomials and degeneracy loci for the classical groups.

Uses Software

• Maple
• ACE

Cites Work

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• Vertex operators and \(\tau\)-functions. Transformation groups for soliton equations. II
• Transformation groups of soliton equations. IV: A new hierarchy of soliton equations of KP-type
• Pieri formula for \(SO_{2n+1}/U_ n\) and \(Sp_ n/U_ n\)
• Décompositions dans l'algèbre des différences divisées. (Decompositions in the algebra of divided differences)
• Pieri type formula for isotropic Grassmannians; the operator approach
• The class of the diagonal in flag bundles
• Plethysm and vertex operators
• Determinantal formulas for orthogonal and symplectic degeneracy loci
• Hall-Littlewood functions and Kostka-Foulkes polynomials in representation theory
• Invariants symétriques entiers des groupes de Weyl et torsion
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• On Certain Symmetric Functions
• Désingularisation des variétés de Schubert généralisées
• Formulas for Lagrangian and orthogonal degeneracy loci; the Q-polynomials approach
• Combinatorial 𝐵_{𝑛}-analogues of Schubert polynomials
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
• Schubert Polynomials for the Classical Groups
• A Note on the Multiplication of Hall Functions
• Modular representations of symmetric groups