Vertex operators arising from Jacobi-Trudi identities

Naihuan Jing, Natasha Rozhkovskaya

Published 2014-11-18Version 1

We give an interpretation of the boson-fermion correspondence as a direct consequence of the Jacobi-Trudi identity. This viewpoint enables us to formulate a unified theory of generalized Schur symmetric functions and obtain a generalized Giambelli identity. It also allows us to construct the action of the Clifford algebra (fermions) on the polynomial algebra from a generalized version of the Jacobi-Trudi identity. As applications, we obtain explicit vertex operators corresponding to characters of the classical Lie algebras, shifted Schur functions, and generalized Schur symmetric functions associated to linear recurrence relations.