  Adler had shown in 1979 that the Toda system can be given a coad- joint orbit
description. We quantize the Toda system by viewing it as a single orbit of a
multiplicative group of lower triangular matrices of determinant one with pos-
itive diagonal entries. We get a unitary representation of the group with
square integrable polarized sections of the quantization as the module . We
find the Rawnsley coherent states after a completion of the above space of
sections. We also find non-unitary finite dimensional quantum Hilbert spaces
for the system.
