This material has been published in J. Combin. Theory Ser. A 77 (1997), 3-50, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier B.V. This material may not be copied or reposted without explicit permission.

Markus Fulmek and Christian Krattenthaler

Lattice path proofs for determinant formulas for symplectic and orthogonal characters

(41 pages)

Abstract. 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-Sharkaway's symplectic tableaux, Proctor's odd and intermediate symplectic tableaux, Proctor's and King and Welsh's orthogonal tableaux, and Sundaram's 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.

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