  We develop graphical calculation methods. Jones-Wenzl projectors for
U_q(sl(2,C)) 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(sl(2,C)) has significant
meaning and it is called 3j symbols. Using single clasp expansions for
U_q(sl(3,C)), we find some trihedron coefficients of the representation theory
of U_q(sl(3,C)). We study representation theory for U_q(sl(4,C)). We conjecture
a complete set of relations for U_q(sl(4,C)).
