Combinatorial properties of Temperley Lieb algebras

Abstract

We consider 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. We study these polynomials from a combinatorial point of view. More precisely we obtain recursions, non recursive formulas, symmetry properties, and expressions for the constant terms, of these polynomials.

This work is based on the author's doctoral dissertation, written under the direction of Prof. F. Brenti at the University of Rome "Tor Vergata"

References in corpus (2)

• The Temperley-Lieb algebra and its generalizations in the Potts and XXZ models
• Teleportation, Braid Group and Temperley--Lieb Algebra