Matrices of Finite Lorentz Transformations in a Noncompact Basis. I. Discrete Series of O(2, 1)

We consider the problem of obtaining the matrices that represent finite group elements in unitary irreducible representations of the group O(2, 1), in a basis in which the ``noncompact'' generator of an O(1, 1) subgroup is diagonal. The discrete series of representations is treated and expressions obtained for the matrix elements of group elements belonging both to the O(2) subgroup and the other O(1, 1) subgroup.