  We give an interpretation of the boson-fermion correspondence as a direct
consequence of Jacobi-Trudi identity. This viewpoint enables us to construct
from a generalized version of the Jacobi-Trudi identity the action of Clifford
algebra on polynomial algebras that arrives as analogues of the algebra of
symmetric functions. A generalized Giambelli identity is also proved to follow
from that identity. As applications, we obtain explicit formulas for vertex
operators corresponding to characters of the classical Lie algebras, shifted
Schur functions, and generalized Schur symmetric functions associated to linear
recurrence relations.
