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Determinantal forms for symplectic and orthogonal Schur functions

Published:1997-04-01
Printed: Apr 1997
• A. M. Hamel
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Abstract

Symplectic and orthogonal Schur functions can be defined combinatorially in a manner similar to the classical Schur functions. This paper demonstrates that they can also be expressed as determinants. These determinants are generated using planar decompositions of tableaux into strips and the equivalence of these determinants to symplectic or orthogonal Schur functions is established by Gessel-Viennot lattice path techniques. Results for rational (also called {\it composite}) Schur functions are also obtained.
 MSC Classifications: 05E05 - Symmetric functions and generalizations 05E10 - Combinatorial aspects of representation theory [See also 20C30] 20C33 - Representations of finite groups of Lie type