The ring of multisymmetric functions
نویسندگان
چکیده
Abstract. Let R be a commutative ring and let n,m be two positive integers. Let AR(n,m) be the polynomial ring in the commuting independent variables xi(j) with i = 1, . . . , m ; j = 1, . . . , n and coefficients in R. The symmetric group on n letters Sn acts on AR(n,m) by means of σ(xi(j)) = xi(σ(j)) for all σ ∈ Sn and i = 1, . . . , m ; j = 1, . . . , n. Let us denote by AR(n,m) Sn the ring of invariants for this action: its elements are usually called multisymmetric functions and they are the usual symmetric functions when m = 1. In this paper we give a presentation of AR(n,m) Sn in terms of generators and relations that holds for any R and any n,m, thereby answering a classical question.
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