Polynomial deformations of $osp(1/2)$ and generalized parabosons

Abstract

We consider the algebra $R$ generated by three elements $A,B,H$ subject to three relations $[H,A]=A$, $[H,B]=-B$ and $\{A,B\}=f(H)$. When $f(H)=H$ this coincides with the Lie superalgebra $osp(1/2)$; when $f$ is a polynomial we speak of polynomial deformations of $osp(1/2)$. Irreducible representations of $R$ are described, and in the case $°(f)\le 2$ we obtain a complete classification, showing some similarities but also some interesting differences with the usual $osp(1/2)$ representations. The relation with deformed oscillator algebras is discussed, leading to the interpretation of $R$ as a generalized paraboson algebra.

18 pages, LaTeX, TWI-94-XX

Cited by in corpus (6)

• Quadratic Poisson algebras for two dimensional classical superintegrable systems and quadratic associative algebras for quantum superintegrable systems
• Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
• The quantum superalgebra $U_q[osp(1/2n)]$: deformed para-Bose operators and root of unity representations
• Three dimensional quadratic algebras: Some realizations and representations
• Jordan-Schwinger realizations of three-dimensional polynomial algebras
• Representations of quadratic Heisenberg-Weyl algebras and polynomials in the fourth Painlevé transcendent