Cyclic representations of q-boson algebra and their applications to quantum algebras and quantum superalgebras

Abstract

In this paper the representation theory of q-boson algebra in the non-generic case thatq is a root of unity is studied from a purely mathematical point of view. Emphasis is placed on its cyclic representations. Various cyclic representations of the q-boson algebra are thereby constructed in explicit form. Using them, we obtain the cyclic representations of quantum superalgebrasU qosp (1, 2),U qosp(1, 4) and quantum algebra (C 2)q through the q-deformed-boson realization method.