Relationship between elliptic polynomial representative models

Determine the precise relationship between the polynomial representatives for elliptic Schubert classes introduced by Rimányi and Weber and the polynomial representative model constructed in the paper, including the relationship between their respective weight functions in type A.

Background

The paper constructs polynomial representatives for its elliptic Schubert classes in type A using weighted generic pipe dreams, extending the pipe-dream models for double Schubert and Grothendieck polynomials. It also compares its elliptic Schubert classes with classes introduced in earlier work by Rimányi and Weber and by Kuroki, Rimányi, and Weber, emphasizing that the classes are different.

The authors note that polynomial representatives for the earlier elliptic classes can also be obtained through weight functions, but leave unresolved how those weight-function constructions are related to the generic-pipe-dream model developed here. Establishing this relationship would clarify the connections between the distinct normalizations and constructions of elliptic Schubert classes.