Specht modules with abelian vertices |
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Authors: | Kay Jin Lim |
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Affiliation: | 1. Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore
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Abstract: | In this article, we consider indecomposable Specht modules with abelian vertices. We show that the corresponding partitions are necessarily p 2-cores where p is the characteristic of the underlying field. Furthermore, in the case of p≥3, or p=2 and μ is 2-regular, we show that the complexity of the Specht module S μ is precisely the p-weight of the partition μ. In the latter case, we classify Specht modules with abelian vertices. For some applications of the above results, we extend a result of M. Wildon and compute the vertices of the Specht module S(pp)S^{(p^{p})} for p≥3. |
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