ABSTRACT
This chapter discusses other irreducible representations of SU(3) and presents some useful general things about the irreducible representations of Lie algebras. We can compute the norms of the states and the action of the raising and lowering operators on the states is built in by construction. The norm of any state can be easily computed using the commutation relations of the simple root generators. Once we have the norms and the matrix elements, we can construct an orthonormal basis in the Hilbert space using the Gram-Schmidt procedure. The orthonormal basis is all we need to complete the construction of the space. We can obtain additional transformations that leave the roots unchanged by combining two or more such reflections. The individual reflections are called Weyl reflections.
