Double Schubert polynomials for the classical groups
By Takeshi Ikeda, Leonardo Constantin Mihalcea, H. Naruse. 2008
68 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/87c1405dd5cb8d1acb324038a6abe5a209886aa3
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Citations in the corpus
- k-Schur Functions and Affine Schubert Calculus (2013, unknown): “Fl in classical type: BCD double Schubert polynomials [65].”
- Introduction to Equivariant Cohomology in Algebraic Geometry (IMPANGA 2010) (2011, background): “ngian and orthogonal Grassmannians, which are homogeneous spaces Sp2n/P and SO2n/P. Working directly in equivariant cohomology, Ikeda et al. have given equivariant Giambelli formulas for these spaces [IMN]. Thom polynomials. The theory of Thom polynomials is one of the origins of equivariant techniq”