Specht Modules and Simple Modules for Centralizer Algebras of the Symmetric Group |
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Authors: | Craig J. Dodge Harald Ellers |
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Affiliation: | 1. Department of Mathematics, Allegheny College, Meadville, Pennsylvania, USAcdodge2@allegheny.edu;3. Department of Mathematics, Allegheny College, Meadville, Pennsylvania, USA |
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Abstract: | Let Σn be the symmetric group on n letters. For l ≤ n identify Σl with a subgroup of Σn in the natural way. Let k be an algebraically closed field of characteristic p. This article begins to develop a theory for modules over the centralizer algebras kΣnΣl that is analogous to James's theory of permutation modules, Specht modules, and simple modules over kΣn. We make a conjecture about how to construct all simple kΣnΣl-modules, we develop tools to test the conjecture, and we prove that it is correct for all n when l < p. |
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Keywords: | Centralizer algebra Simple modules Specht modules Symmetric group |
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