Representations of the Quantum Group $SL_q(2)$ in a Space of Functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 374-381 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct representations of the quantum group $SL_q(2)$ in a functional space. We consider the cases of general and exceptional values of the deformation parameter $q$.
Keywords: quantum deformation, cyclic representation, Casimir operators.
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D. R. Karakhanyan. Representations of the Quantum Group $SL_q(2)$ in a Space of Functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 374-381. http://geodesic.mathdoc.fr/item/TMF_2003_134_3_a3/

[1] L. D. Faddeev, N. Yu. Reshetikhin, L. A. Takhtadzhyan, Algebra i analiz, 1:1 (1989), 178 | MR

[2] S. Derkachov, D. Karakhanyan, R. Kirschner, Nucl. Phys. B, 583 (2000), 691 ; 618 (2001), 589 ; D. Karakhanyan, R. Kirschner, M. Mirumyan, Nucl. Phys. B, 636 (2002), 529 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[3] P. P. Kulish, E. K. Sklyanin, TMF, 40 (1979), 194 ; V. G. Drinfel'd, “Quantum groups”, Proc. Intl. Congress of Mathematicians (Berkeley, California, 1986), ed. A. M. Gleason, AMS, Providence, RI, 1987, 798 | MR

[4] E. K. Sklyanin, Funkts. analiz i ego prilozh., 17:4 (1983), 34 | MR | Zbl

[5] L. Alvarez-Gaume, C. Gomes, G. Sierra, Nucl. Phys. B, 330 (1990), 347 | DOI | MR | Zbl

[6] T. Hakobyan, A. Sedrakyan, Mod. Phys. Lett. A, 10 (1995), 495 | DOI | MR | Zbl

[7] P. W. Wiegmann, A. V. Zabrodin, Mod. Phys. Lett. A, 2 (1987), 893 | DOI

[8] C. De Concini, V. G. Kac, “Representations of quantum groups at roots of 1”, Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory, Proc. Colloq. in Honour of J. Dixmier (Paris, 22–26 May, 1989), Progr. Math., 92, eds. A. Connes, M. Duflo, A. Joseph, R. Rentschler, Birkhäuser, Boston, MA, 1990, 471 ; D. Arnaudon, P. Roche, Lett. Math. Phys., 17 (1989), 295 | MR | DOI | MR | Zbl