Combinatorial properties of the Temperley-Lieb algebra of a Coxeter group
J. Algebr. Comb. 37(4), 717-736 (2013)
Summary: 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.
temperley-Lieb algebra, Hecke algebra, Kazhdan-Lusztig basis, Coxeter group