Polynomial deformations of osp(1/2) and generalized parabosons
نویسنده
چکیده
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 deg(f) ≤ 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. Senior Research Associate of N.F.W.O. (National Fund for Scientific Research of Belgium). Permanent address : The Institute of Mathematical Sciences, Madras 600 113, India.
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