The factorial Schur function

The application of the divided difference of a function to the inhomogeneous symmetric functions (factorial Schur functions) of Biedenharn and Louck is shown to lead to new relations and simplified proofs of their properties. These results include determinantal definitions and the factorial Jacobi–T...

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Bibliographic Details
Published in:Journal of mathematical physics 1993-09, Vol.34 (9), p.4144-4160
Main Authors: Chen, William Y. C., Louck, James D.
Format: Article
Language:English
Subjects:
662120 - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-)
Algebraic methods
Classical and quantum physics: mechanics and fields
CLEBSCH-GORDAN COEFFICIENTS
Exact sciences and technology
FUNCTIONS
GROUP THEORY
HYPERGEOMETRIC FUNCTIONS
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICS
MATRICES
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Quantum mechanics
ROTATIONAL INVARIANCE
SYMMETRY GROUPS
UNITARITY
WIGNER COEFFICIENTS
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Summary:The application of the divided difference of a function to the inhomogeneous symmetric functions (factorial Schur functions) of Biedenharn and Louck is shown to lead to new relations and simplified proofs of their properties. These results include determinantal definitions and the factorial Jacobi–Trudi identities with extensions to skew versions. Similar properties of a second class of symmetric functions depending on an arbitrary parameter, and of importance for generalized hypergeometric functions and series, are shown also to be derivable from the divided difference notion, slightly extended.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.530032