Covexillary Schubert varieties and Kazhdan-Lusztig Polynomials

TL;DR

This paper develops combinatorial and inductive formulas for Kazhdan-Lusztig polynomials related to covexillary elements in classical types, extending previous results for Grassmannians using intersection cohomology and variety isomorphisms.

Contribution

It introduces new formulas for Kazhdan-Lusztig polynomials for covexillary elements, broadening understanding in classical types beyond Grassmannians.

Findings

Derived combinatorial formulas for covexillary Kazhdan-Lusztig polynomials

Extended previous Grassmannian results to classical types

Utilized intersection cohomology and variety isomorphisms in proofs

Abstract

We establish combinatorial and inductive formulas for Kazhdan-Lusztig polynomials associated to covexillary elements in classical types, extending results of Boe, Lascoux-Sch\"{u}tzenberger, Sankaran-Vanchinathan, and Zelevinsky for Grassmannians of classical types. The proof uses intersection cohomology theory and the isomorphism of Kazhdan-Lusztig varieties from Anderson-Ikeda-Jeon-Kawago.