An orthogonal realization of representations of the Temperley–Lieb algebra

Abstract

Under a suitable hypothesis, we construct a full set of pairwise orthogonal maximal vectors in V⊗n, where V=V(1) is the simple module of highest weight 1 for the quantized enveloping algebra U(sl2). We give a number of applications, one of which is an orthogonal basis of the simple modules for the Temperley–Lieb algebra TLn. We relate this new orthogonal basis to the standard cellular basis.