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Apr 15, 2014 at 13:25 comment added Geordie Williamson One can also prove that the number of orbits are the same using the Fourier transform. It gives a canonical isomorphism $Fun(V) \to Fun(V^*)$ and hence $Fun_G(V) \to Fun_G(V^*)$. The dimensions of both sides is the number of $G$-orbits.
Aug 2, 2013 at 11:15 vote accept Amritanshu Prasad
Aug 2, 2013 at 9:54 answer added Jeremy Rickard timeline score: 21
Aug 2, 2013 at 9:10 history asked Amritanshu Prasad CC BY-SA 3.0