From sl q (2) to a Parabosonic Hopf Algebra

[摘要] A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations are developed. Designated by sl −1 (2), this algebra encompasses the Lie superalgebra osp (1|2). It is obtained as a q =−1 limit of the sl q (2) algebra and seen to be equivalent to the parabosonic oscillator algebra in irreducible representations. It possesses a noncocommutative coproduct. The Clebsch-Gordan coefficients (CGC) of sl −1 (2) are obtained and expressed in terms of the dual −1 Hahn polynomials. A generating function for the CGC is derived using a Bargmann realization.

[关键词] parabosonic algebra;dual Hahn polynomials;Clebsch–Gordan coef ficients