Oscillator Representations of the Lie Algebra su(1, 1) and the Quantum Algebra suq(1, 1)

Abstract

It is discussed how the representations of the Lie algebra su(1, 1) and its q-deformation su q (1, 1) are constructed in terms of operators a, a + and N satisfying [N, a] = −a, [N, a + ] = a + and N + = N. It is found that any irreducible unitary representation of su(1, 1) and su q (1, 1) can be described by a, a + and N in an infinite number of ways