Let $V_\lambda$ be the irreducible representation of $sl_{n}(\mathfrak{C})$ with highest weight $\lambda$. There are well known formulas for the decomposition of $V_\lambda^{\otimes^k}= V_\lambda\otimes V_\lambda\otimes \cdots\otimes V_\lambda$ into irreducble representations using Littelwood-Richardson, or Littelmann paths, among others.

Is there any similar for the symmetric power $S^k(V_\lambda)$ or for $\wedge^k(V_\lambda)$, even for $sl_2(\mathfrak{C})$ or$k=3, 4$, or just some results in some cases??

I know that small cases can be computed, for instance using LiE http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/form.html but this formulas seems to be recursive. Is there any closed formula like Littelwood-Richardson, or Littelmann paths?

What is the best recent reference?

Thanks

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