  Following on from a general observation in an earlier paper, we consider the
continuous symmetries of a certain class of conformal field theories
constructed from lattices and their reflection-twisted orbifolds. It is shown
that the naive expectation that the only such (inner) symmetries are generated
by the modes of the vertex operators corresponding to the states of unit
conformal weight obtains, and a criterion for this expectation to hold in
general is proposed.
