Vertices of simple modules for the symmetric groups in blocks of small weights.
The authors determine the vertices and sources of the simple modules in 2-blocks of finite symmetric groups of weight \(w\leq 4\), and in 3-blocks of finite symmetric groups of weight \(w\leq 3\). Whereas the number of isomorphism classes of these simple modules depends only on the weight of the corresponding block, the vertices and sources of these simple modules also depend on the Scopes equivalence class of the block. Reviewer's remark: The one vertex which remained open in the paper under review, and its source have since been determined: [the authors and the reviewer, J. Algebra 320, No. 2, 680-707 (2008; Zbl 1161.20006)].
scientific article; zbMATH DE number 5345497
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