Double eta polynomials and equivariant Giambelli formulas

TL;DR

This paper introduces double eta polynomials using Young's raising operators, providing explicit formulas for equivariant Schubert classes in even orthogonal Grassmannians and connecting to existing eta polynomials.

Contribution

It develops double eta polynomials as an orthogonal analogue of double theta polynomials, offering new Giambelli formulas for equivariant cohomology.

Findings

Provides explicit Giambelli formulas for equivariant Schubert classes

Introduces double eta polynomials as an orthogonal analogue

Connects double eta polynomials to existing eta polynomials

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.