  In this paper, we consider two different subjects: the algebra of universal
characters $S_{[\lambda,\mu]}({\bf x},{\bf y})$ (a generalization of Schur
functions) and the phase model of strongly correlated bosons. We find that the
two-site generalized phase model can be realized in the algebra of universal
characters, and the entries in the monodromy matrix of the phase model can be
represented by the vertex operators $\Gamma_i^\pm(z) (i=1,2)$ which generate
universal characters. Meanwhile, we find that these vertex operators can also
be used to obtain the A-model topological string partition function on $\mathbb
C^3$.
