| Autor: |
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov |
| Jazyk: |
angličtina |
| Rok vydání: |
2011 |
| Předmět: |
|
| Zdroj: |
Symmetry, Integrability and Geometry: Methods and Applications, Vol 7, p 093 (2011) |
| Druh dokumentu: |
article |
| ISSN: |
1815-0659 |
| DOI: |
10.3842/SIGMA.2011.093 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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