Elliptic classes on Langlands dual flag varieties

TL;DR

This paper establishes a novel symmetry between elliptic classes of Schubert varieties on a flag variety and its Langlands dual, revealing deeper geometric and combinatorial insights at the elliptic level.

Contribution

It introduces a new symmetry relating elliptic classes on dual flag varieties, extending Schubert calculus beyond cohomology and K-theory.

Findings

Identifies a relation between elliptic classes on dual flag varieties.

Reveals symmetry only apparent at the elliptic level.

Enhances understanding of Schubert calculus in advanced cohomological theories.

Abstract

Characteristic classes of Schubert varieties can be used to study the geometry and the combinatorics of homogeneous spaces. We prove a relation between elliptic classes of Schubert varieties on a generalized full flag variety and those on its Langlands dual. This new symmetry is only revealed if Schubert calculus is elevated from cohomology or K theory to the elliptic level.