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The Structure of Some Permutation Modules for the Symmetric Group of Infinite Degree

✍ Scribed by Darren G.D. Gray

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 301 KB
Volume: 193
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6963

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✦ Synopsis

Suppose that ⍀ is an infinite set and k is a natural number. Let ⍀ denote the set of all k-subsets of ⍀ and let F be a field. In this paper we study the Ž . w x k FSym ⍀ -submodule structure of the permutation module F ⍀ . Using the representation theory of finite symmetric groups, we show that every submodule of w x k Ž . F ⍀ can be written as an intersection of kernels of certain FSym ⍀ -homomorw x k w x l phisms F ⍀ ª F ⍀ for 0 F lk, and give a simple algorithm to determine w x k the complete submodule structure of F ⍀ .

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