  It is well-known that unitary irreducible representations of groups can be
usefully classified in a 3-fold classification scheme: Real, Complex,
Quaternionic. In 1962 Freeman Dyson pointed out that there is an analogous
10-fold classification of irreducible representations of groups involving both
unitary and antiunitary operators. More recently it was realized that there is
also a 10-fold classification scheme involving superdivision algebras. Here we
give a careful proof of the equivalence of these two 10-fold ways.
