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Uniqueness of representation

richardhp
Post Icon Posted: Submitted by richardhp on 21 February 2010 - 11:41am.

Joined: 2007-10-01
Posts: 239

So, I may be being really stupid here but anyway here goes. Suppose I have a group $ G = < x_1, ... , x_n | R> $ and a representation $ \rho (x_i) = A_i $ defined on each of the generators, with each $ A_i $ satisfying R, then surely this completely determines the representation.

It's just there seem to be a lot of questions along the lines, prove there is a unique representation st $ \rho(x) = A $... etc. and it seems to me that all you have to do is show it is a representation and then uniqueness follows automatically or am I missing something?

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