Author: Francesco Vaccarino
Title:  The ring of multisymmetric functions

2000 Mathematical Subject Classifications: 05E05, 13A50, 20C30
Keywords and Phrases: Characteristic free invariant theory, symmetric functions, representations of symmetric groups

Abstract Text: Let R be a commutative ring and let n,m be two positive integers. The symmetric group on n letters acts diagonally on the ring of polinomia in
nxm variables with coefficients in R. The subrings of invariants for this action is called the ring of multisymmetric functions since these are the usual
symmetric functions when m=1. In this paper we will give a presentation in terms of generators and relations that holds for any R and any n,m answering in
this way to a classical question. I would like to thank M.Brion, C.De Concini and C.Procesi, in alphabetical order, for useful discussions.

status: submitted for publication