$V$ is an $m$ dimensional vector space having a structure of $sl_2(\mathbb{C})$-module, where $sl_2(\mathbb{C})$ is the Lie algebra of the Lie group $SL_2(\mathbb{C})$. The symmetric group $S_n$ acts on the tensor product $V^{\otimes n}$.
What does Schur-Weyl duality say in this case?
What is the irreducible decomposition of $V^{\otimes n}$?
If we have $S_n$ irreducible decomposition can we get $sl_2(\mathbb{C})$ decomposition and vice versa?
I would be very grateful if someone could give a detailed answer. Thanking you in advance.