Factorial P- and Q-Schur functions represent equivariant quantum Schubert classes

TL;DR

This paper provides explicit presentations and polynomial representatives for the equivariant quantum cohomology rings of maximal isotropic Grassmannians, connecting Schubert classes with factorial P- and Q-Schur functions.

Contribution

It introduces new generators, relations, and Pfaffian formulas for these cohomology rings, linking algebraic geometry with symmetric function theory.

Findings

Presentations by generators and relations for the rings.

Polynomial representatives for Schubert classes using Pfaffian formulas.

Interpretation of formulas in terms of Chern classes.

Abstract

We find presentations by generators and relations for the equivariant quantum cohomology rings of the maximal isotropic Grassmannians of types B,C and D, and we find polynomial representatives for the Schubert classes in these rings. These representatives are given in terms of the same Pfaffian formulas which appear in the theory of factorial $P$- and $Q$-Schur functions. After specializing to equivariant cohomology, we interpret the resulting presentations and Pfaffian formulas in terms of Chern classes of tautological bundles.