  There is a unique finite group that lies inside the 2-dimensional unitary
group but not in the special unitary group, and maps by the symmetric square to
an irreducible subgroup of the 3-dimensional real special orthogonal group. In
an earlier paper I showed how the representation theory of this group over the
real numbers gives rise to much of the structure of the standard model of
particle physics, but with a number of added twists. In this theory the group
is quantised, but the representations are not. In this paper I consider how a
quantisation of the representations might lead to a more fundamental theory.
