Kazhdan-Lusztig polynomials of boolean elements

TL;DR

This paper derives explicit combinatorial formulas for Kazhdan-Lusztig polynomials and their parabolic analogues for boolean elements within Coxeter groups with tree-structured Coxeter graphs.

Contribution

It provides the first closed-form combinatorial product formulas for these polynomials in the specified setting, extending previous theoretical work.

Findings

Explicit formulas for Kazhdan-Lusztig polynomials of boolean elements

Formulas applicable to Coxeter groups with tree graphs

Advances understanding of polynomial structure in specific Coxeter groups

Abstract

We give closed combinatorial product formulas for Kazhdan-Lusztig poynomials and their parabolic analogue of type q in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan-Lusztig theory, J. Algebra 295 (2006)], in Coxeter groups whose Coxeter graph is a tree.