Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 27-51 (1999)

Multisymmetric Functions

John Dalbec

Department of Mathematics, Yale University, 10 Hillhouse Ave., P. O. Box 208283, New Haven CT 06520-8283, USA

Abstract: We develop a theory of multisymmetric functions along the lines of the theory of ordinary symmetric functions presented in [M]. We extend this theory to the multihomogeneous case (factorizable forms) in characteristic $0$. In addition, we present proofs of several results that appear in [J] without proof, as well as counterexamples to some claims made therein.

[M] Macdonald, Ian G.: Symmetric Functions and Hall Polynomials. Oxford University Press, New York 1979. \smallskip [J] Junker, F.: Über symmetrische Funktionen von mehreren Reihen von Veränderlichen. Math. Ann. 43 (1893), 225-270.

Classification (MSC91): 05E05

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