Vertex operators, Weyl determinant formulae and Littlewood duality

TL;DR

This paper explores vertex operator realizations of symplectic and orthogonal Schur functions, providing new proofs of determinant identities and duality relations, advancing understanding in algebraic combinatorics and representation theory.

Contribution

It introduces new proofs of determinant identities and duality for symplectic and orthogonal Schur functions using vertex operator techniques.

Findings

New vertex operator realizations of symplectic and orthogonal Schur functions

Alternative proofs of determinant identities for group characters

A novel proof of the duality between orthogonal and symplectic Schur functions

Abstract

Vertex operator realizations of symplectic and orthogonal Schur functions are studied and expanded. New proofs of determinant identities of irreducible characters for the symplectic and orthogonal groups are given. We also give a new proof of the duality between the universal orthogonal and symplectic Schur functions using vertex operators.