The structure of some permutation modules for the symmetric group of infinite degree

[摘要] Suppose that Omega is an infinite set and k is a natural number. Let [Omega](k) denote the set of all k-subsets of Omega and let F be a field. In this paper we study the FSym(Omega)-submodule structure of the permutation module F[Omega](k). Using the representation theory of finite symmetric groups, we show that every submodule of F[Omega](k) can be written as an intersection of kernels of certain FSym(Omega)-homomorphisms F[Omega](k) --> F[Omega](l) for 0 less than or equal to l < k, and give a simple algorithm to determine the complete submodule structure of F[Omega](k). (C) 1997 Academic Press.

[发布日期] 1997-07-01