  We define an extension of the affine Brauer algebra, the type B/C affine
Brauer algebra. This new algebra contains the hyperoctahedral group and it
naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and
Symplectic groups. Thus we obtain a compact analogue of Schur-Weyl duality. We
study functors $F_{\mu,k}$ from the category of admissible $O(p,q)$ or
$Sp_{2n}(\mathbb{R})$ modules to representations of the type B/C affine Brauer
algebra $\mathfrak{B}_k^\theta$. Thus providing a Akawaka-Suzuki-esque link
between $O(p,q)$ (or $Sp_{2n}(\mathbb{R})$) and $\mathfrak{B}_k^\theta$.
Furthermore these functors take non spherical principal series modules to
principal series modules for the graded Hecke algebra of type $D_k$, $C_{n-k}$
or $B_{n-k}$. With this we get a functorial correspondence between admissible
simple $O(p,q)$ (or $Sp_{2n}(\mathbb{R})$) modules and graded Hecke algebra
modules.
