A new approach to the $S{L}_n$ spider

Abstract

The $S{L}_n$ spider gives a diagrammatic way to encode the representation category of the quantum group $U_q(s{l}_n)$. The aim of this paper is to define a new spider that contains the $S{L}_n$ spider. The new spider is defined by generators and relations, according to fairly simple rules that start with combinatorial data coming from the root system of $S{L}_n$.

13 pages, 6 figures