According to Schur--Weyl duality, the centralizer of $\mathrm{GL}(V)$ acting diagonally on $V^{\otimes N}$ is the group algebra of the symmetric group $\mathbb S_N$. An equivalent formulation is the existence of a decomposition $$ V^{\otimes N} \cong \bigoplus_\lambda s_\lambda \otimes V_\lambda $$ where $s_\lambda$ (resp. $V_\lambda$) denote irreducible representations of $\mathbb S_N$ (resp. $\mathrm{GL}(V)$), and $\lambda$ ranges over partitions of $N$.
If we suppose that $V$ has a bilinear form and replace $\mathrm {GL}(V)$ by $\mathrm O(V)$, then the centralizer is a quotient of the Brauer algebra $B_N$. The analogous decomposition reads $$ V^{\otimes N} \cong \bigoplus_\lambda \pi_\lambda \otimes V_{\langle \lambda \rangle} $$ where $\pi_\lambda$ (resp. $V_{\langle \lambda \rangle}$) denote irreducible representations of $B_N$ (resp. $\mathrm{O}(V)$), and $\lambda$ ranges over partitions of $N - 2k$, $k \geq 0$.
In the group algebra of $\mathbb S_N$, there are explicit idempotents whose images are the irreducibles $s_\lambda$, called Young symmetrizers. What's the analogue in $B_N$? Is there a formula for an idempotent in $B_N$ which projects onto $\pi_\lambda$?