The q-analog of the boson algebra, its representation on the Fock space, and applications to the quantum group.

In this paper, a realization of the q-deformed boson operators on the Fock space from a generally algebraic point of view is given. The representations of the quantum group (Cn)q are thereby constructed in terms of this realization. Some infinite- and finite-dimensional representations of the q-analog of the Heisenberg–Weyl algebra are obtained on certain quotient spaces. Finally, the q-deformed differential realization of quantum group given by Alvarez-Gaume, Gomez, and Sierra (Preprint CERN-Th 5369/89) is derived from the boson realization. [ABSTRACT FROM AUTHOR]