Billey-Type Formula for KL-Schubert Classes in Hyperbolic Cohomology

TL;DR

This paper develops a Billey-type formula for KL-Schubert classes within hyperbolic cohomology, extending the understanding of these classes in the context of flag varieties and Grassmannians.

Contribution

It introduces a novel Billey-type formula for KL-Schubert classes in hyperbolic cohomology, expanding computational tools for these classes.

Findings

Established Poincaré dualities for KL-Schubert classes.

Derived a Billey-type formula for KL-Schubert classes in hyperbolic cohomology.

Focused on Grassmannians to illustrate the formula.

Abstract

This paper studies the KL-Schubert classes defined by Kazhdan-Lusztig bases in $K$-theory and hyperbolic cohomology of flag varieties. We first establish Poincar\'e dualities of these classes. We then focus on Grassmannians, and establish the Billey-type formula for KL-Schubert classes in hyperbolic cohomology.