A new approach to the $SL_n$ spider

Abstract: The $SL_n$ spider gives a diagrammatic way to encode the representation category of the quantum group $U_q(sl_n)$. The aim of this paper is to define a new spider that contains the $SL_n$ 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 $SL_n$.