多重对称函数环
The ring of multisymmetric functions
摘要：
设R是交换环，n，m是两个正整数. n个字母上的对称群对角地作用在系数为R的n × m元多项式环上。这个作用的不变量的子环被称为多对称函数环，因为当m=1时，这些是通常的对称函数。在本文中，我们将给出一个演示的发电机和关系，适用于任何R和任何n，m回答以这种方式一个经典的问题。我谨按字母顺序感谢布里翁先生、德孔西尼先生和普罗切西先生进行了有益的讨论。
英文摘要：
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 polynomials 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
