Timeline for Is the projector to irreducible tensor modules of SO(N) known?
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| Sep 6, 2014 at 17:53 | comment | added | Vít Tuček | It is a bit unclear what exactly are you asking for. For $\mathrm{GL}(n, \mathbb{C})$ the theory of Schur functors give projectors to all irreducible submodules of $\otimes^k \mathbb{C}^n$. For the orthogonal or symplectic group it works in the same way on the space of harmonic tensors which are the subspace of of the full tensor power on which all traces are zero. So you can first project to harmonic tensors and then use a Schur functor. | |
| Sep 5, 2014 at 13:28 | comment | added | Grobi Grobsen | Thanks, but I did not see an explicit formula for the projectors or a way to extract them from this. Am I missing something? | |
| Sep 4, 2014 at 16:23 | comment | added | Vít Tuček | See Symmetry, Representations, and Invariants by Goodman and Wallach. The decomposition of tensor you are looking for are in Appendix F, which is freely available on Goodman's website: math.rutgers.edu/~goodman/repbook.html | |
| Sep 4, 2014 at 15:57 | review | First posts | |||
| Sep 4, 2014 at 15:57 | |||||
| Sep 4, 2014 at 15:53 | history | asked | Grobi Grobsen | CC BY-SA 3.0 |