Abstract
A bosonic operator of Uq(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of Uq(osp(1|2)) for q a root of unity (in the unrestricted specialisation). As in the classical case, it also simplifies the classification of finite dimensional irreducible representations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Rosso, M.: Analogues de la forme de Killing et du théorème d'Harish-Chandra pour les groupes quantiques, Ann. Sci. École Norm. Sup. (4) 23 (1990), 445.
Lusztig, G.: Modular representations and quantum groups, Contemp. Math. 82 (1989), 59.
De Concini, C. and Kac, V. G.: Representations of Quantum Groups at Roots of 1, Progress in Math. 92, Birkhäuser, Basel, 1990, p. 471.
Kerler, T.: Darstellungen der Quantengruppen und Anwendungen, Diplomarbeit, ETH-Zurich, August 1989.
Arnaudon, D. and Bauer, M.: Polynomial relations in the centre of Uq (sl(N)), Lett. Math. Phys. 30 (1994), 251 (hep-th/9310030).
Abdesselam, B., Arnaudon, D. and Chakrabarti, A.: Representations of Uq (sl(N)) at roots of unity, J. Phys. A: Math. Gen. 28 (1995), 5495 (q-alg/9504006).
Kac, V. G.: Representations of classical Lie superalgebras, in: Lecture Notes in Math. 676, Springer-Verlag, Berlin, Heidelberg, New York, 1978.
Abdesselam, B., Arnaudon, D. and Bauer, M.: 1)) at roots of unity, q-alg/9605015, ENSLAPP-A-583/96.
Kulish, P. P. and Reshetikhin, N. Yu: 2), Lett. Math. Phys. 18 (1989), 143-149.
Leśniewski, A.: A remark on the Casimir elements of Lie superalgebras and quantized Lie superalgebras, J. Math. Phys. 36 (3) (1995), 1457.
Pais, A. and Rittenberg, V.: Semisimple graded Lie algebras, J. Math. Phys. 16 (1975), 2062.
Pinczon, G.: 2), J. Algebra 132 (1990),219.
Arnaudon, D., Bauer, M. and Frappat, L.: On Casimir's ghost, q-alg/9605021, ENSLAPP-A-587/96.
Duflo, M.: Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbrede Lie semi-simple, Ann. of Math. (2) 105 (1977), 107.
Musson, I. M.: A classification of primitive ideals in the enveloping algebra of a classical simple Lie superalgebra, Adv. in Math. 91 (1992), 252.
Zhang, R. B.: 2n)) and its connection with quantum so(2n + 1), Lett. Math. Phys. 25 (1992), 317.
Kassel, C.: Quantum Groups, Graduate Texts in Math 155, Springer Verlag 1995.
Kobayashi, K.-I.: 2)q, Z. Phys. C 59 (1993), 155.
Palev, T. D.: and Stoilova, N. I.: Unitarizable representations of the deformed parabose superalgebra Uq (osp(1/2)) at roots of 1, J. Phys. A 28 (1995), 7275 (q-alg/9507026).
Ge Mo-Lin, Sun Chang-Pu and Xue Kang: New R-matrices for the Yang-Baxter equation associated with the representations of the quantum superalgebra Uq (osp(1, 2)) with q a root of unity, Phys. Lett. A 163 (1992), 176.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Arnaudon, D., Bauer, M. Scasimir Operator, Scentre and Representations of Uq(osp(1|2)). Letters in Mathematical Physics 40, 307–320 (1997). https://doi.org/10.1023/A:1007359625264
Issue Date:
DOI: https://doi.org/10.1023/A:1007359625264