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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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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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description	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.
doi_str_mv	10.1063/1.530032
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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
title	The factorial Schur function
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