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knowwhatyoudontknow

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- TL;DR Summary
- Tensor decomposition, Sym[SUB]n[/SUB] representations and irreps.

New to group theory. I have 3 questions:

1. Tensor decomposition into T

2. The Sym

3. What is the connection between Sym

1. Tensor decomposition into T

_{ab}= T_{[ab]}+T^{(traceless)}_{{ab}}+ Tr(T_{{ab}}) leads to invariant subspaces. Is this enough to imply these subreps are irreducible?2. The Sym

^{n}representations of a group are irreps. Why?3. What is the connection between Sym

^{n}representations and tensor decomposition?