Double Schubert polynomials for the classical groups

Abstract

For each infinite series of the classical Lie groups of type B,C or D, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the appropriate flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynomials of Billey and Haiman, which represent non-equivariant Schubert classes. They are also positive in a certain sense, and when indexed by maximal Grassmannian elements, or by the longest element in a finite Weyl group, these polynomials can be expressed in terms of the factorial analogues of Schur's Q- or P-functions defined earlier by Ivanov.

41 pages, 2 tables; comments welcome

References in corpus (2)

• A Schubert calculus recurrence from the noncomplex W-action on G/B
• Permutation actions on equivariant cohomology

Cited by in corpus (22)

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• Left Demazure-Lusztig operators on equivariant (quantum) cohomology and K theory
• Double eta polynomials and equivariant Giambelli formulas
• Double theta polynomials and equivariant Giambelli formulas
• Construction of double Grothendieck polynomials of classical types using IdCoxeter algebras
• The universal factorial Hall-Littlewood $P$- and $Q$-functions
• Pipe dreams for Schubert polynomials of the classical groups
• Double Grothendieck Polynomials for Symplectic and Odd Orthogonal Grassmannians
• Factorial P- and Q-Schur functions represent equivariant quantum Schubert classes
• Pfaffian sum formula for the symplectic Grassmannians
• Generalized (co)homology of the loop spaces of classical groups and the universal factorial Schur $P$- and $Q$-functions
• A Giambelli formula for classical $G/P$ spaces
• Gröbner bases, symmetric matrices, and type C Kazhdan-Lusztig varieties
• Degeneracy locus formulas for amenable Weyl group elements
• The A.B.C.Ds of Schubert calculus
• Introduction to Equivariant Cohomology in Algebraic Geometry (IMPANGA 2010)
• Infinite flags and Schubert polynomials
• On the K-theoretic fundamental classes of Deligne-Lusztig varieties
• A tableau formula for vexillary Schubert polynomials in type C