  We consider in this note Furstenberg transformations on Cartesian products of
infinite-dimensional tori. Under some appropriate assumptions, we show that
these transformations are uniquely ergodic with respect to the Haar measure and
have countable Lebesgue spectrum in a suitable subspace. These results
generalise to the infinite-dimensional setting previous results of H.
Furstenberg, A. Iwanik, M. Lemanzyk, D. Rudolph and the second author in the
one-dimensional setting. Our proofs rely on the use of commutator methods for
unitary operators and Bruhat functions on the infinite-dimensional torus.
