  The hook components of $V^{\otimes n}$ interpolate between the symmetric
power $\sym^n(V)$ and the exterior power $\wedge^n(V)$. When $V$ is the vector
space of $k\times m$ matrices over $\bbc$, we decompose the hook components
into irreducible $GL_k(\bbc)\times GL_m(\bbc)$-modules. In particular,
classical theorems are proved as boundary cases. For the algebra of square
matrices over $\bbc$, a bivariate interpolation is presented and studied.
