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Determinantal Forms for Symplectic and Orthogonal Schur Functions

Published online by Cambridge University Press:  20 November 2018

A. M. Hamel
A. M. Hamel*
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand e-mail: physamh@phys.canterbury.ac.nz
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Abstract

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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 composite) Schur functions are also obtained.

Keywords

05E0505E1020C33
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 263 - 282
Copyright
Copyright © Canadian Mathematical Society 1997

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