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@pm: what holds for GL(2)? the SO(2)xDiag(2)xSO_K(2) decomp.? No I'm not sure at all. 3 dimensions was the only example I had been thinking of. I should have said K is positive definite, sorry. So basically its either SO(3) on both sides or SO_K(3) on both sides and the mixed decomposition is impossible?
