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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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