Conjugation Modules for Symmetric Groups

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• William O'Donovan, Royal Holloway
• Friday 04 November 2016, 15:00-16:00
• CMS, MR15.

If you have a question about this talk, please contact Nicolas Dupré.

The study of the structure of permutation modules for symmetric groups over fields of positive characteristic is an active area of research in the modular representation theory of symmetric groups. In this talk, I will introduce a family of permutation modules for the symmetric group S_{pn}, the so-called conjugation modules, obtained by inducing the trivial module for the wreath product C_p \wr S_n to S_{pn}. I will present results parametrising the vertices of the conjugation modules (and explain the modular representation theory background, e.g. the definition of a vertex of a module) , and outline a connection to Foulkes’ Conjecture, one of the most important open problems in the characteristic zero representation theory of the symmetric group.

This talk is part of the Junior Algebra and Number Theory seminar series.

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