Title: Boson-fermion correspondence in the language of symmetric functions
Speaker: Natalia Rojkovskaia (Kansas State University)
Abstract: We give an interpretation of the boson-fermion correspondence as a direct consequence of the Jacobi - Trudi identity. This viewpoint enables us to construct the action of the Clifford algebra (fermions) on the polynomials algebra from a generalized version of the Jacobi - Trudi identity. As applications, we obtain explicit vertex operators that correspond to characters of the classical Lie algebras, shifted Schur functions, and generalized Schur symmetric functions associated to linear recurrence relations.