Specht modules with abelian vertices
Kay Jin Lim
DOI: 10.1007/s10801-011-0298-0
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\geq 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 ( p p) S^{(p^{p})} for p\geq 3.
Pages: 157–171
Keywords: keywords Specht module; vertex; complexity
Full Text: PDF
References
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6. Carlson, J.: The varieties and the cohomology ring of a module. J. Algebra 85, 104-143 (1983)
7. Chuang, J., Tan, K.M.: On Young modules of defect 2 blocks of symmetric group algebras. J. Algebra 221, 651-668 (1999)
8. Danz, S., Külshammer, B., Zimmermann, R.: On vertices of simple modules for symmetric groups of small degrees. J. Algebra 320, 680-707 (2008)
9. Donkin, S.: Symmetric and exterior powers, linear source modules and representations of Schur superalgebras. Proc. Lond. Math. Soc. 83, 647-680 (2001)
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15. Hemmer, D.: The complexity of certain Specht modules for the symmetric group. J. Algebr. Comb.
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