Quantum Groups and Quantum Algebras
in Nuclear Physics Context

Quantum groups and algebras receive recently an increasing interest among both the mathematicians and physicists. Some "mechanical" applications of the quantum groups to nuclear superdeformation (consisting in a successful fit of the SU_q(2) based formula to the experiment) are known in the literature but do not allow for a deeper insight into the nuclear structure.

We would like to construct and study these quantum Lie algebras whose traditional partner-algebras have interesting interpretations in the nuclear physics context. In particular the quantum-deformed SO(5)-algebra (SO(5) corresponding to the proton-neutron pairing problem) and a quantum-deformed correspondent of the rigid-rotor seem as an interesting starting point. In this case we would like to construct the irreducible representations and Casimir operators related to the above algebras and apply the implied classifications of the solutions to the dynamical problems of motion (spectra and their properties).