Deformed Heisenberg algebra with reflection Original Research Article

A universality of the deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional representations of parafermionic nature. We demonstrate that finite-dimensional representations are representations of the deformed parafermionic algebra with internal Z2-grading structure. On the other hand, any finite- or infinite-dimensional representation of the algebra supplies us with irreducible representations of the osp(1|2) superalgebra. We show that the normalized form of the deformed Heisenberg algebra with reflection has the structure of a guon algebra related to the generalized statistics.