A2-web immanants

We describe the rank 3 Temperley–Lieb–Martin algebras in terms of Kuperberg’s A 2 -webs. We define consistent labelings of webs and use them to describe the coefficients of decompositions into reduced webs. We introduce web immanants, inspired by Temperley–Lieb immanants of Rhoades and Skandera. We show that web immanants are positive when evaluated on totally positive matrices and describe some further properties.