Kazhdan Lusztig and R polynomials of generalized Temperley Lieb algebras

TL;DR

This paper investigates two polynomial families in generalized Temperley-Lieb algebras, providing recursions, formulas, and properties, especially for non-branching Coxeter graphs, extending understanding of algebraic combinatorics.

Contribution

It introduces and analyzes polynomial families analogous to Kazhdan-Lusztig and R polynomials within generalized Temperley-Lieb algebras, with new recursive and combinatorial results.

Findings

Derived recursions for the polynomials

Established closed-form formulas

Explored properties for non-branching Coxeter graphs

Abstract

We study two families of polynomials that play the same role, in the generalized Temperley Lieb algebra of a Coxeter group, as the Kazhdan Lusztig and R polynomials in the Hecke algebra of the group. Our results include recursions, closed formulas, and other combinatorial properties for these polynomials. We focus mainly on non branching Coxeter graphs.