If I have, for example a particle with $s = 3/2$ and $\ell = 2$, what are the allowed values of $j$? I'm slightly confused because I know that $j = \ell + s$, so surely there is only one allowed value?

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Check this out: Clebsch-Gordan coefficients. –  lomppi Apr 12 '13 at 16:48

The problem is that $\ell$ and $s$ are the eigenvalues of the angular momentum, but each value of them corresponds to multiple underlying states (unless the eigenvalue is zero). In effect the eigenvalue represents the magnitude of a vector angular momentum, but not it's direction, and the various different underlying states represent different possible values of direction.