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SUMMARY:Conjugation Modules for Symmetric Groups - William O'Donovan\, Roy
 al Holloway
DTSTART:20161104T150000Z
DTEND:20161104T160000Z
UID:TALK68226@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:The study of the structure of permutation modules for symmetri
 c groups over fields of positive characteristic is an active area of resea
 rch in the modular representation theory of symmetric groups. In this talk
 \, I will introduce a family of permutation modules for the symmetric grou
 p S_{pn}\, the so-called conjugation modules\, obtained by inducing the tr
 ivial 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 explai
 n the modular representation theory background\, e.g. the definition of a 
 vertex of a module) \, and outline a connection to Foulkes' Conjecture\, o
 ne of the most important open problems in the characteristic zero represen
 tation theory of the symmetric group.
LOCATION:CMS\, MR15
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