  Using the vertex operator representations for symplectic and orthogonal Schur
functions, we define two families of symmetric functions and show thatthey are
the skew symplectic and skew orthogonal Schur polynomials defined implicitly by
Koike and Terada and satisfy the general branching rules. Furthermore, we
derive the Jacobi-Trudi identities and Gelfand-Tsetlin patterns for these
symmetric functions. Additionally, the vertex operator method yields their
Cauchy-type identities. This demonstrates that vertex operator representations
serve not only as a tool for studying symmetric functions but also offers
unified realizations for skew Schur functions of types A, C, and D.
