Hook length products and Cayley operators of classical invariant theory

We show how hook length products of frames associated with integral partitions are involved in the evaluation of the Cayley operators of classical invariant theory. In this setting, hook length products play a more fundamental role than they do in the representation theory of the symmetric group. We give an elementary combinatorial argument which derives the result of Frame, Robinson and Thrall 2] concerning the dimensions of the irreducible representations of the symmetric group from these same general results of invariant theory.