Isomorphisms between Quantum Group Covariant q-Oscillator Systems Defined for q and 1/q

Abstract

It is shown that there exists an isomorphism between q-oscillator systems covariant under $S{U}_q(n)$ and $S{U}_{q^{-1}}(n)$. By the isomorphism, the defining relations of $S{U}_{q^{-1}}(n)$ covariant q-oscillator system are transmuted into those of $S{U}_q(n)$. It is also shown that the similar isomorphism exists for the system of q-oscillators covariant under the quantum supergroup $S{U}_q(n/m)$. Furthermore the cases of q-deformed Lie (super)algebras constructed from covariant q-oscillator systems are considered. The isomorphisms between q-deformed Lie (super)algebras can not obtained by the direct generalization of the one for covariant q-oscillator systems.

LaTeX 13pages, RCNP-070

References in corpus (2)

• Algebraic Structures Related to Reflection Equations
• A Classically Singular Representation of $s{u}_q(n)$