I am following the Quantum Mechanics I, Galindo A., Pascual P. and in page 207 explaining the matrix representations of the Rotation Operators in the angular momentum it appears the next (obvious) equation:
Being $\alpha,\beta,\gamma$ the Euler angles, $J$ the value for the total angular momentum (orbital+spin) and $M$ corresponding to the eigen value of $J_z$.
I don't understand the physical meaning of the equations. I mean, on the left part it is applying the rotation operator to the state vector $|JM\rangle$. As $J$ is invariant under rotations the right part of the equation should be obvious. So, what is the right part of the equation telling me? Maybe I'm getting confused with the Dirac notation. Any tip?