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Dec 30, 2010 at 23:53 comment added Deane Yang I would add that I have no idea how to deal with an arbitrary subgroup $G$ of the group of diffeomorphisms. A more reasonable and more useful question is to ask about tensors or subspaces of tensors (at a fixed point in the manifold) that are invariant under a subgroup of $GL(v)$ (for example, $SL(v)$, $O(n)$, $U(n/2)$ for $n$ even, etc.).
Dec 30, 2010 at 20:34 comment added Willie Wong To give a reference, much of the last paragraph is explained in H. Weyl, The classical groups, their invariants and representations.
Dec 30, 2010 at 20:07 comment added Deane Yang MathJax remains an inscrutable mystery to me.
Dec 30, 2010 at 20:06 history answered Deane Yang CC BY-SA 2.5