  Dimensional reduction of maximal supergravity to two dimensions leads to an
infinite-dimensional (non-local) symmetry group W x E_9 which has a simpler
action when the bosonic fields are dualised to an infinite tower of dual
potentials. We construct a doubled-valued representation of its compact
subgroup K x K(E_9) and we show that off-shell fermions take place in this
infinite-dimensional representation. The equations of motion can be written in
a fully gauge-covariant way as a selfduality condition for the
infinite-dimensional fields. The W x E_9 global symmetry is thus manifest. The
linear system associated to the theory is recovered in a triangular gauge.
Finally we provide supersymmetry transformations for off-shell fields.
