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From slq(2) to a Parabosonic Hopf Algebra
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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From slq(2) to a Parabosonic Hopf Algebra
Інший ID:
2010 Mathematics Subject Classification: 17B37; 17B80; 33C45
Посилання:
From slq(2) to a Parabosonic Hopf Algebra / S. Tsujimoto, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ.
Підтримка:
The authors are grateful to M.S. Plyushchay for drawing their attention to [5] and [14]. The
authors would like to gratefully acknowledge the hospitality extended to LV and AZ by Kyoto University and to ST and LV by the Donetsk Institute for Physics and Technology in the course of this investigation. The research of ST is supported in part through funds provided by KAKENHI (22540224), JSPS. The research of LV is supported in part by a research grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada.
Дата:
2011
Переглядів:
493
Завантажень:
242
Анотація:
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 slq(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.
