On the Vertices of Simple Modules for Symmetric Groups

Abstract

In this article, we are concerned with the computation of vertices of some series of simple modules for the symmetric group of n letters in odd characteristic. In the first, the second, and the third section of this work we recall some more or less general results that are needed in our proofs. The fourth section contains new ingredients (in terms of dimension) that play an important role in our proofs of the main results in the last section.

Key Words:

• Blocks
• Simple modules
• Symmetric groups
• Vertices

2000 Mathematics Subject Classification:

• 20C30
• 20C20

ACKNOWLEDGMENT

The results here are part of the results of the author's doctoral thesis Fotsing (2007) including some generalizations. The author would like to thank his advisor Prof. B. Külshammer for his support during the last four years. Also the author is very grateful to the Friedrich–Ebert–Stiftung for the financial support while his doctoral thesis was written at the Mathematical Institute of the University of Jena.

Notes

Communicated by D. K. Nakano.