SYMMETRIES OF THE QUANTUM STATE-SPACE AND GROUP-REPRESENTATIONS

The homomorphisms of a connected Lie group G into the symmetry group o f a quantum system are classified in terms of unitary representations of a simply connected Lie group associated with G. Moreover, an explic it description of the T-multipliers of G is obtained in terms of the R -multipliers of the universal covering G of G and the characters of G . As an application, the Poincare group and the Galilei group, both i n 3 + 1 and 2 + 1 dimensions, are considered.