  This paper is concerned with the construction of the polynomial tau-functions
of the symplectic KP (SKP), orthogonal KP (OKP) hierarchies and universal
character hierarchy of B-type (BUC hierarchy), which are proved as zero modes
of certain combinations of the generating functions. By applying the strategy
of carrying out the action of the quantum fields on vacuum vector, the
generating functions for symplectic Schur function, orthogonal Schur function
and generalized Q-function have been presented. The remarkable feature is that
polynomial tau-functions are the coefficients of certain family of generating
functions. Furthermore, in terms of the Vandermonde-like identity and
properties of Pfaffian, it is showed that the polynomial tau-functions of the
SKP, OKP and BUC hierarchies canbe written as determinant and Pfaffian forms,
respectively. In addition, the soliton solutions of the SKP and OKP hierarchies
have been discussed.
