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

Key Points

• This work aims to explore the construction of representations of the Lie algebra su(1, 1) and its quantum deformation suq(1, 1).
• Discussed operators a, at, and N satisfying specific commutation relations.
• Analyzed irreducible unitary representations using algebraic relationships.
• Demonstrated infinite representation descriptions for both algebras.
• Found that representations of both algebras can be described in infinitely many ways.
• Confirmed the consistency of the constructed representations with quantum algebra relations.