Let $V=\mathbb{R}^n$ and $O(n)$ the orthogonal group acting with its standard action on $V$. Now for any partition $\lambda$ we have the Schur module $S_\lambda V$ which is a representation of $O(n)$. Unlike in the case of the general linear group, these are not irreducible as $O(n)$-modules (for example $\textrm{Sym}^2V$ decomposes to multiples of the identity matrix and the traceless symmetric matrices). Is there a general description/recipe on how the $O(n)$-module $S_\lambda V$ decomposes into irreducible ones? If not in general, maybe for some interesting (and not too special) types of partitions?