The Representation Theory of the finite and infinite Temperley-Lieb algebras

The Temperley-Lieb algebras are a family of finite dimensional algebras that are quotients of the symmetric groups algebras, or more generally the Iwahori-Hecke algebras. They appear in a number of areas of mathematics, including statistical mechanics, knot theory, quantum groups, and subfactors. We review their representation theory and give some results on an infinite dimensional generalization.