Let $V$ be a $n$-dimensional real vector space equipped with a positively definite scalar product $g$ and let $\mathrm{O}(n)$ be the automorphism group of $(V,g)$. View $V^{\otimes k}$ as a $\mathrm{O}(n)$-module via the diagonal action. I am interested in the following specific submodules, which arise from Riemannian geometry and affine differential geometry:

(1) $ \mathscr{R}(V)=\{R\in V^{\otimes 4}\mid\mathrm{Cyc}_{12}(R)=\mathrm{Cyc}_{34}(R)=\mathrm{Cyc}_{234}(R)=0\} $. Here $\mathrm{Cyc}_{234}: V^{\otimes4}\rightarrow V^{\otimes 4} $ is the $\mathrm{O}(n)$-module morphism which averages cyclic permutations of the 2nd, 3rd and 4th components, $$ \mathrm{Cyc}_{234}(x_1\otimes x_2\otimes x_3\otimes x_4)=\frac{1}{3}\left(x_1\otimes x_2\otimes x_3\otimes x_4+x_1\otimes x_3\otimes x_4\otimes x_2+x_1\otimes x_4\otimes x_2\otimes x_3\right). $$ $\mathrm{Cyc}_{12}$ is defined similarly. $\mathscr{R}(V)$ is the space where Riemannian curvature tensors live.

(2) $ \mathscr{C}(V)=\{R\in V^{\otimes 4}\mid \mathrm{Tr}_{12}(R)=0,\, \mathrm{Cyc}_{34}(R)=\mathrm{Cyc}_{234}(R)=0\}. $ Here $\mathrm{Tr}_{12}: V^{\otimes 4}\rightarrow V\otimes V$ contracts the 1st and 2nd components through $g$. $\mathscr{C}(V)$ is the space where curvature tensors of torsion-free volume-preserving affine connections on a Riemannian manifold live.

(3) $ \mathscr{A}(V)=\{A\in V^{\otimes3}\mid\mathrm{Cyc}_{12}(A)=A, \, \rm{Tr}_{23}(A)=0\} $, the space where the difference tensor of two torsion-free volume-preserving affine connections lives.

The decomposition of $\mathscr{R}(V)$ into irreducible $\mathrm{O}(n)$-modules is well known under the name "Ricci decomposition" and is discussed briefly in the book "Einstein Manifolds" by Besse. The decomposition of $\mathscr{C}(V)$ seems obtained only recently by Blazic, Gilkey, Nikcevic, and Simon. I can't find any reference for the decomposition of $\mathscr{A}(V)$. So my question is

(1) Where exactly can I find a systematic treatment of the decomposition problem for this kind of $\mathrm{O}(n)$-modules?

(2) In particular, given a $\mathrm{O}(n)$-module $W$ like the above ones, i.e. a submodule of $V^{\otimes k}$ which is the kernel of some $\mathrm{Tr}$ and $\mathrm{Cyc}$ type morphisms, is there a general algorithm, or strategy, to decompose $W$ into irreducible pieces?

(3) In particular, has a irreducible decomposition of $\mathscr{A}(V)$ appeared in the literature?