  In this paper, we firstly give the definition of the coupled Hall-Littlewood
function and its realization in terms of vertex operators. Then we construct
the representation of the two-site generalized $q$-boson model in the algebra
of coupled Hall-Littlewood functions. Finally, we find that the vertex
operators which generate coupled Hall-Littlewood functions can also be used to
obtain the partition function of the A-model topological string on the
conifold.
