  The fermionic Fock space admits two different actions of the quantized
enveloping algebra of $\hat\sln$> The first one is a q-deformation of the
well-known level-one representation of the affine Lie algebra and the second
one is a new level-zero action arising from solvable lattices models. In this
paper we prove that these two constructions can be glued together to get a
representation of a new object: the toridal quantum group. This representation
involves some difference operatorators. It is due to the fact that the
specialization at q=1 of the toroidal algebra is isomorphic to the enveloping
algebra of the universal central extension of a current algebra over a quantum
torus.
