Lattice Path Proofs for Determinantal Formulas for Symplectic and Orthogonal Characters

We give bijective proofs for Jacobi–Trudi-type and Giambelli-type identities for symplectic and orthogonal characters. These proofs base on interpreting King and El-Sharkawayʹs symplectic tableaux, Proctorʹs odd and intermediate symplectic tableaux, Proctorʹs and King and Welshʹs orthogonal tableaux, and Sundaramʹs odd orthogonal tableaux in terms of certain families of nonintersecting lattice paths. This work is intended to be the counterpart of the Gessel–Viennot proof of the Jacobi–Trudi identities for Schur functions for the case of symplectic and orthogonal characters.