Murphy bases of generalized Temperley-Lieb algebras

Abstract.

In this article we show how to use some results of G. E. Murphy on the so-called standard basis of Hecke-Algebras of Type A to derive a similar basis for generalized Temperley-Lieb algebras. This standard basis is compared to the usual diagrammatic basis of the original Temperley-Lieb algebra used in knot theory and statistical physics.