From slq(2) to a Parabosonic Hopf Algebra

Satoshi Tsujimoto
2011 Symmetry, Integrability and Geometry: Methods and Applications  
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
more » ... 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.
doi:10.3842/sigma.2011.093 fatcat:j2phohecznfohgayid3khkfp5q