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Given a field F, FS_{4}is a group algebra... we have a representation X that maps FS_{4}to 3x3 matrices over (presumably) F. Let V denote the FS_{4}module corresponding to X..... do stuff. My question is, what the heck is V supposed to be?

I assumed that V is F^{3}, but that seemingly contradicts what the question wants me to do. So is V the free module of the representation of FS_{4}over itself (and then why bother having a representation)? I can't think of what else it could be

The full question can be found at

http://www.maths.ox.ac.uk/courses/2...a-introduction-representation-theory/material

sheet 5, question 3

EDIT: I was wrong... if V=F^{3}the question's conclusion is correct. For some reason I was associating the 4 in S_{4}with F instead, and thought it had characteristic 4... I noticed my error when I realized a) it has characteristic 0 b) 4 isn't the characteristic of a field. Good job by me wasting an hour working in a non-existent field

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# Homework Help: Terminology issue regarding modules and representations

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