The field of definition will be the complex numbers, $V$ is a vector space of dimension $m$, and $O(V)$ is the orthogonal group preserving some nondegenerate bilinear form on $V$. The centralizer algebra of $O(V)$ acting on $V^{\otimes f}$ is a quotient of the Brauer algebra, and there is a decomposition of the form

$V^{\otimes f} = \bigoplus_{\lambda} S_{[\lambda]} V \otimes \pi_\lambda$

where $\lambda$ ranges over all partitions of size $f - 2k$, where $0 \le k \le f/2$, $S_{[\lambda]} V$ is an irrep for the orthogonal group, and $\pi_\lambda$ is an irrep for the centralizer algebra.

I would like to have an explicit construction for $\pi_\lambda$ similar to the Specht modules for the symmetric group, i.e., given by generators and relations, preferably where the generators are given by some combinatorial objects. Is this written down somewhere? The dimension of $\pi_\lambda$ is essentially the number of oscillating tableaux of shape $\lambda$, so a source that touches on that would also be appreciated.