Double theta polynomials and equivariant Giambelli formulas

Abstract

We use Young's raising operators to introduce and study double theta polynomials, which specialize to both the theta polynomials of Buch, Kresch, and Tamvakis, and to double (or factorial) Schur S-polynomials and Q-polynomials. These double theta polynomials give Giambelli formulas which represent the equivariant Schubert classes in the torus-equivariant cohomology ring of symplectic Grassmannians, and we employ them to obtain a new presentation of this ring in terms of intrinsic generators and relations.

25 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