1997/01/19 by Mikhail S. Plyushchay, Mikhail Plyushchay
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cellular algebra #Filtered algebra #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Reflection (computer programming) #Superalgebra #Symmetric algebra #Universality (dynamical systems) #cond-mat #hep-th #math.QA #q-alg
paper · pdf · doi:10.1016/s0550-3213(97)00065-5
published as Nucl.Phys. B491 (1997) 619-634 · 16 pages, LaTeX, to appear in Nucl. Phys. B
arxiv created 1997/01/19 · openalex publication_date 1997/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Z2-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.