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The ring of multisymmetric functions. (English) Zbl 1062.05143

Summary: We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring \(R\), thereby answering a classical question coming from works of F. Junker in the late nineteen century and then implicitly in H. Weyl’s book [The classical groups, their invariants and representation (Princeton University Press, Princeton, N.J.) (1939; Zbl 0020.20601)].

MSC:

05E05 Symmetric functions and generalizations
13A50 Actions of groups on commutative rings; invariant theory
20C30 Representations of finite symmetric groups
05E10 Combinatorial aspects of representation theory

Citations:

Zbl 0020.20601
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References:

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