  We give a complete set of generators for the discrete exceptional U-duality
groups of toroidal compactified type II theory and M-theory in d>2. For this,
we use the DSZ quantization in d=4 as originally proposed by Hull and Townsend,
and determine the discrete group inducing integer shifts on the charge lattice.
It is generated by fundamental unipotents, which are constructed by
exponentiating the Chevalley generators of the corresponding Lie algebra. We
then extend a method suggested by the above authors and used by Sen for the
heterotic string to get the discrete U-duality group in d=3, thereby obtaining
a quantized symmetry in d=3 from a d=4 quantization condition. This is studied
first in a toy model, corresponding to d=5 simple supergravity, and then
applied to M-theory. It turns out that, in the toy model, the resulting
U-duality group in d=3 is strictly smaller than the one generated by the
fundamental unipotents corresponding to all Chevalley generators. However, for
M-theory, both groups agree. We illustrate the compactification to d=3 by an
embedding of d=4 particle multiplets into the d=3 theory.
