Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-01-19
Nucl.Phys. B491 (1997) 619-634
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, LaTeX, to appear in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(97)00065-5
A universality of 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 the parafermionic nature. We demonstrate that finite-dimensional representations are representations of deformed parafermionic algebra with internal Z_2-grading structure. On the other hand, any finite- or infinite-dimensional representation of the algebra supply us with irreducible representation of osp(1|2) superalgebra. We show that the normalized form of deformed Heisenberg algebra with reflection has the structure of guon algebra related to the generalized statistics.
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