Combinatorial properties of the Temperley-Lieb Algebra of a Coxeter group

Abstract

We study two families of polynomials that play the same role in the Temperley-Lieb algebra of a Coxeter group as the Kazhdan-Lusztig and R-polynomials play in the Hecke algebra of the group. Our results include recursions, non-recursive formulas, symmetry properties and expressions for the constant term. We focus mainly on non-branching Coxeter graphs. © Springer Science+Business Media, LLC 2012.