  Based on the Riemann fractional derivative the Casimir operators and
multipletts for the fractional extension of the rotation group SO(n) are
calculated algebraically. The spectrum of the corresponding fractional
symmetric rigid rotor is discussed. It is shown, that the rotational,
vibrational and $\gamma$-unstable limits of the standard geometric collective
models are particular limits of this spectrum. A comparison with the ground
state band spectra of nuclei shows an agreement with experimental data better
than 2%. The derived results indicate, that the fractional symmetric rigid
rotor is an appropriate tool for a description of low energy nuclear
excitations.
