Vertex operators and Giambelli identities

We use the Jacobi-Trudi identity to incorporate several well-known families of symmetric functions to uniformly treat generalized Schur symmetric functions and their vertex operator realization. Under the general set-up, we prove that Gambelli identity also holds, thus derive several scattered results under one umbrella. In particular, this includes Weyl's character formulas of classical simple Lie algebras and the shifted Schur symmetric functions studied by Olshanski-Okounkov. This is joint work with Natasha Rozhkovskaya.Non UBCUnreviewedAuthor affiliation: North Carolina State UniversityFacult