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May 5, 2012 at 17:32 comment added Henri Johnston A very nice answer - thanks! If I understand correctly: under the given hypotheses, by combining your argument with its `dual' we in fact have $\dim_k W^G=1 \Leftrightarrow W≅k[G] \Leftrightarrow dim_k W_G = 1$.
May 5, 2012 at 17:13 vote accept Henri Johnston
May 4, 2012 at 16:31 comment added Joël Nice answer, modp !
May 4, 2012 at 16:28 history answered modp CC BY-SA 3.0