Abstract
James classified the simple modules over the group algebra using modules denoted , where is a partition of . In particular, he showed that is simple or zero for every partition and, furthermore, that for every simple -module there exists a partition such that . This paper is an extension of a paper of Dodge and Ellers in which they studied analogous modules over the centralizer algebra , where is a partition of and a partition of . For every positive prime we find counterexamples to their conjecture that the -modules are always simple or zero, where is a field of characteristic . We also study the relationship between and in special cases.
Citation
Craig Dodge. Harald Ellers. Yukihide Nakada. Kelly Pohland. "Some nonsimple modules for centralizer algebras of the symmetric group." Involve 9 (5) 877 - 898, 2016. https://doi.org/10.2140/involve.2016.9.877
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