Abstract

We develop graphical calculation methods. Jones-Wenzl projectors for U_q) are very powerful tools to find not only invariants of links but also invariants of 3-manifolds. We find single clasp expansions of generalized Jones-Wenzl projectors for simple Lie algebras of rank 2. Trihedron coefficients of the representation theory for U_q) has significant meaning and it is called 3j symbols. Using single clasp expansions for U_q), we find some trihedron coefficients of the representation theory of U_q). We study representation theory for U_q). We conjecture a complete set of relations for U_q).