Character Relations and Simple Modules in the Auslander–Reiten Graph of the Symmetric and Alternating Groups and their Covering Groups
by Bessenrodt, C.; Uno, K.
From character relations for symmetric groups or Hecke algebras such as the Murnaghan–Nakayama formula and the Jantzen–Schaper formula, we obtain a lower bound for the diagonal entries of Cartan matrices. Moreover, we prove an analogous character relation for covering groups of symmetric groups and obtain a similar lower bound. As an application, we show in these situations that for wild blocks simple modules must lie at the end of the Auslander–Reiten quiver, which is equivalent to the fact that the hearts of projective indecomposable modules are indecomposable.
DOI: 10.1023/A:1012701002315
Print publication date: 12/1/2001
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