  This paper is a tutorial in a general and explicit procedure to simplify
semidefinite programs which are invariant under the action of a symmetry group.
The procedure is based on basic notions of representation theory of finite
groups. As an example we derive the block diagonalization of the Terwilliger
algebra of the binary Hamming scheme in this framework. Here its connection to
the orthogonal Hahn and Krawtchouk polynomials becomes visible.
