  The theorem of orthogonal-orthogonal duality of Rowe, Repka, and Carvalho is
proven by a method based on characters that is very different from theirs and
akin to Helmers's half a century earlier proof of the analogous
sympletic-symplectic duality. I demonstrate how three duality theorems listed
by Rowe, Repka, and Carvalho allow very brief derivations of linear relations
between the Casimir invariants of the connected representations based on the
geometry of their Young diagrams, and discuss for which physical systems other
than such already considered in the literature an analysis in terms of the
orthogonal-orthogonal duality might be useful.
