The Structure of Some Permutation Modules for the Symmetric Group of Innnite Degree
نویسنده
چکیده
Suppose that is an innnite set and k is a natural number. Let ] k denote the set of all k-subsets of and let F be a eld. In this paper we study the FSym(()-submodule structure of the permutation module F] k. Using the representation theory of nite symmetric groups, we show that every submodule of F] k can be written as an intersection of kernels of certain FSym(()-homomorphisms F] k ?! F] l for 0 l < k, and give a simple algorithm to determine the complete submodule structure of F] k .
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