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The angle-angular momentum quantum phase space is considered and the corresponding Heisenberg - Weyl group is studied. When (2j+1) is a power of a prime, Z(2j+1) is a Galois field and stronger results can be proved. SL(2,Z(2j+1)) transformations are explicitly constructed and various properties of the displacement operators are studied. Central extensions of the Abelian group by Z(2j+1) are studied and they provide all the ways of constructing the Heisenberg - Weyl group from G and Z(2j+1).
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Apostol Vourdas (1996) studied this question.
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