From $sl_q(2)$ to a Parabosonic Hopf Algebra
Mathematical Physics
2011-10-10 v3 Classical Analysis and ODEs
math.MP
Abstract
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 , this algebra encompasses the Lie superalgebra . It is obtained as a limit of the 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 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
Cite
@article{arxiv.1108.1603,
title = {From $sl_q(2)$ to a Parabosonic Hopf Algebra},
author = {Satoshi Tsujimoto and Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:1108.1603},
year = {2011}
}