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Theoretical discussion on how to construct representations of su(1, 1) and its q-deformation suq(1, 1), suggesting infinite representation methods.
It is discussed how the representations of the Lie algebra su(l, 1) and its q-deformation sUq(l, 1) are constructed in terms of operators a, at and N satisfying [N, a] =-a, [N, at]=a t and Nt =N. It is found that any irreducible unitary representation of su(l, i) and suil, 1) can be described by a, at and N in an infinite number of ways.
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Hirayama et al. (1993) studied this question.
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