Double eta polynomials and equivariant Giambelli formulas

Abstract

We use Young's raising operators to introduce and study double eta polynomials, which are an even orthogonal analogue of Wilson's double theta polynomials. Our double eta polynomials give Giambelli formulas which represent the equivariant Schubert classes in the torus-equivariant cohomology ring of even orthogonal Grassmannians, and specialize to the single eta polynomials of Buch, Kresch, and the author.

22 pages; final version

References in corpus (7)

• Degeneracy Loci Classes in $K$-theory - Determinantal and Pfaffian Formula -
• Chern class formulas for classical-type degeneracy loci
• Double eta polynomials and equivariant Giambelli formulas
• Double theta polynomials and equivariant Giambelli formulas
• Interpolation analogues of Schur Q-functions
• Factorial P- and Q-Schur functions represent equivariant quantum Schubert classes
• Pfaffian sum formula for the symplectic Grassmannians

Cited by in corpus (8)

• Degeneracy Loci Classes in $K$-theory - Determinantal and Pfaffian Formula -
• Chern class formulas for classical-type degeneracy loci
• Double theta polynomials and equivariant Giambelli formulas
• Double eta polynomials and equivariant Giambelli formulas
• Double Grothendieck Polynomials for Symplectic and Odd Orthogonal Grassmannians
• Degeneracy locus formulas for amenable Weyl group elements
• Integral homology of real isotropic and odd orthogonal Grassmannians
• Symplectic and odd orthogonal Pfaffian formulas for algebraic cobordism