Representations of the Infinite-Dimensional Affine Group

We introdu e an in nite-dimensional a ne group and onstru t its irredu ible unitary representation. Our approa h follows the one used by Vershik, Gelfand and Graev for the di eomorphism group, but with modi ations made ne - essary by the fa t that the group does not a t on the phase spa e. However it is possible to de ne its a tion on some lasses of fun tions.