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Multisymmetric functions. (English) Zbl 0953.05077

Summary: We develop a theory of multisymmetric functions along the lines of the theory of ordinary symmetric functions presented in I. G. Macdonald [Symmetric functions and Hall polynomials (Oxford Mathematical Monographs. Oxford: Clarendon Press) (1979; Zbl 0487.20007)]. We extend this theory to the multihomogeneous case (factorizable forms) in characteristic \(0\). In addition, we present proofs of several results that appeared in F. Junker [Über symmetrische Funktionen von mehreren Reihen von Veränderlichen, Math. Ann. 43, 225-270 (1893)] without proof, as well as counterexamples to some claims made therein.

MSC:

05E05 Symmetric functions and generalizations

Citations:

Zbl 0487.20007
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