Double eta polynomials and equivariant Giambelli formulas (Q2822145)

Let \(k\) be a positive integer and \(OG = OG(n-k, 2n)\) be the Grassmannian that parametrizes isotropic subspaces of dimension \(n-k\) in the vector space \(\mathbb C^{2n}\), equipped with an orthogonal form. The eta polynomials \(H_{\lambda}(c)\) of Buch, Kresch, and the author are Giambelli polynomials that represent the Schubert classes in the cohomology ring of \(OG\).NEWLINENEWLINEIn this paper using Young raising operators the author defines double eta polynomials \(H_{\lambda}(c|t)\), which represent the equivariant Schubert classes in the equivariant cohomology ring \({H^\ast}_T (OG)\), where \(T\) is a maximal torus of the complex even orthogonal group.