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 motivated by 3D mirror symmetry, and it is only revealed if Schubert calculus is elevated from cohomology or K theory to the elliptic level.

中文翻译：

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朗兰兹双旗品种的椭圆类

舒伯特变体的特征类可用于研究齐次空间的几何学和组合学。我们证明了广义满旗变体上舒伯特变体的椭圆类与其朗兰兹对偶上的椭圆类之间的关系。这种新的对称性是由 3D 镜像对称性推动的，只有当舒伯特微积分从上同调或 K 理论提升到椭圆水平时才会显示出来。