Let $$U \mapsto U \otimes U^\* \otimes U \otimes U^\*$$ be a unitary representation of the unitary group $U(n)$ acting on the vector space $V$ (where $U^\*$ is the complex conjugate of $U$). We can decompose $V$ into invariant subspaces in which the representation is irreducible. Let $P\_i$'s be projectors onto invariant subspaces. I want to find these projectors explicitly and use them in a numerical calculation.


Is there any way to do this? like an algorithm for generating them numerically?



Projectors onto the invariant subspaces of a unitary representation $U \otimes U^* \otimes U \otimes U^*$
One way to do this is to solve the Clebsch-Gordan problem. [This](http://arxiv.org/abs/1009.0437) paper discusses an algorithm for this on the unitary group.


A similar question was asked earlier (see [here](https://mathoverflow.net/questions/198022/decomposing-a-reducible-representation-of-the-unitary-group/198222#198222)). I posted an answer there that might also be useful.


