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From $sl_q(2)$ to a Parabosonic Hopf Algebra
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: parabosonic algebra; dual Hahn polynomials; Clebsch–Gordan coefficients. 
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     title = {From $sl_q(2)$ to a {Parabosonic} {Hopf} {Algebra}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a92/}
}
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Satoshi Tsujimoto; Luc Vinet; Alexei Zhedanov. From $sl_q(2)$ to a Parabosonic Hopf Algebra. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a92/

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