[en] The suggestion made by Gell-Mann that the SL(3,R) group may be a useful symmetry in nuclear rotational bands is investigated. By using a phenomenological description of a deformed rotator, differential operators representing the time derivatives of quadrupole moments are constructed and the conditions under which they satisfy the SL(3,R) commutation relations examined. It is then found that there are three sets of unitary irreducible representations of SL(3,R) corresponding to three different classes of rigid rotators. The matrix-elements in each of these classes are evaluated and the results compared with those of the recent investigation by Weaver and Biedenharn. With the help of explicit differential operators representation of the generators of SL(3,R), the computation of the Casimir operators becomes a feasible task, and the invariants have been calculated. It is also shown that this procedure can easily be carried into the double covering group SL(3,R) to yield the half-integer spin bands resorting to a particle-core coupling model. The SL(3,R) and T₅ x SU(2) models for quantum rotators are compared and it is shown that most of the SL(3,R) representations can be obtained from the T₅ x SU(2) representations by means of a generalized Gell-Mann formula. (U.S.)