LATTICE PATH PROOFS FOR DETERMINANTAL FORMULAS FOR SYMPLECTIC AND ORTHOGONAL CHARACTERS

We give bijective proofs for Jacobi-Trudi-type and Giambelli-type iden tities for symplectic and orthogonal characters. These proofs base on interpreting King and El-Sharkaway's symplectic tableaux. Proctor's od d and intermediate symplectic tableaux, Proctor's and King and Welsh's orthogonal tableaus, and Sundaram's odd orthogonal tableaux in terms of certain Families of nonintersecting lattice paths. This work is int ended to be the counterpart of the Gessel-Viennot proof of the Jacobi- Trudi identities for Schur functions For the case of symplectic and or thogonal characters. (C) 1997 Academic press