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When is the algebra of multisymmetric polynomials generated by the elementary multisymmetric polynomials? (English) Zbl 1062.05140
Summary: Multisymmetric polynomials are the $$r$$-fold diagonal invariants of the symmetric group $${\mathfrak{S}}_n$$. Elementary multisymmetric polynomials are analogues of the elementary symmetric polynomials, in the multisymmetric setting. In this paper, we give a necessary and sufficient condition on a ring $$A$$ for the algebra of multisymmetric polynomials with coefficients in $$A$$ to be generated by the elementary multisymmetric polynomials.

MSC:
 05E05 Symmetric functions and generalizations 20C30 Representations of finite symmetric groups 13A50 Actions of groups on commutative rings; invariant theory
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