Equivariant Schubert Calculus for Inverse Grassmannian Permutations

We give a Graham-positive expansion for the product of two double Schubert polynomials indexed by two inverse Grassmannian permutations.

Surprisingly, the nonzero structure constants are double Schubert polynomials in two disjoint sets of equivariant variables.

We also give a positive expansion for the product of two single Schubert polynomials indexed by a $321$-avoiding permutation (e.g., a Grassmannian permutation) and an inverse Grassmannian permutation.

Unexpectedly, the nonzero structure constants are Edelman--Greene coefficients.