Elliptic classes of Schubert varieties

TL;DR

This paper introduces elliptic Borisov-Libgober classes for Schubert varieties, providing new recursive formulas and linking them to elliptic weight functions, advancing elliptic Schubert calculus.

Contribution

It defines new elliptic classes in Schubert calculus, establishes their independence from choices, and connects them to elliptic weight functions through recursion.

Findings

Derived multiplicities of divisors in Schubert varieties.

Established simple recursive formulas for elliptic classes.

Proved that elliptic weight functions represent these classes.

Abstract

We introduce new notions in elliptic Schubert calculus: the (twisted) Borisov-Libgober classes of Schubert varieties in general homogeneous spaces G/P. While these classes do not depend on any choice, they depend on a set of new variables. For the definition of our classes we calculate multiplicities of some divisors in Schubert varieties, which were only known for full flag varieties before. Our approach leads to a simple recursions for the elliptic classes. Comparing this recursion with R-matrix recursions of the so-called elliptic weight functions of Rimanyi-Tarasov-Varchenko we prove that weight functions represent elliptic classes of Schubert varieties.