Abstract
The existence of U q (sl(2)) invariant operators for q P = 1 leads to relations for the quantum Clebsch - Gordan kernels and for the quantum 6j-symbols (= fusion matrices). These relations effectively reduce some equalities, inherited from the generic q case, and imply, in particular, that the polynomial identities for the quantum 6 j -symbols are consistent with the minimal theories chiral fusion rules.
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References
V. Pasquier, Comm. Math. Phys., 118 (1988) 365.
G. Moore and N. Seiberg, Comm. Math. Phys. 123 (1989) 177.
V. Pasquier and H. Saleur, in: E. Brézin, J. Zinn-Justin (eds.), Champs, Cordes et Phénomènes Critiques, Les Houches proceedings 1988, Elsevier Science Publishers (1989).
V. Pasquier and H. Saleur, Saclay preprint SPhT/89-031 (1989).
L. Alvarez-Gaumé, C. Gomez, and G. Sierra, Nucl. Phys. B319 (1989) 155. to appear.
L. Alvarez-Gaumé, C. Gomez, and G. Sierra, Phys. Lett. 220B (1989) 142.
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Nucl. Phys. B241 (1984) 333.
V.S. Dotsenko and V.A. Fateev, Nucl. Phys. B240 [FS12] (1984) 312, and B251 [FS13] (1985) 691, Phys. Lett. 154B (1985) 291.
G. Moore and N. Seiberg, Phys. Lett. B212 (1988) 451.
N.Yu. Reshetikhin, Leningrad preprints LOMI E-4-87, E-17-87 (1987).
A.N. Kirillov and N.Yu. Reshetikhin, Leningrad preprint LOMI E-9-88 (1988).
A. Tsuchiya and Y. Kanie, in: Conformal Field Theory and Solvable Lattice Models, Adv. Studies in Pure Math., 16 (1988) 360.
J. Fröhlich, Cargese Lectures 1987, in: G. 't Hooft et al. (eds), Non-Perturbative Quantum Field Theory, New York, Plenum Press, 1988.
K.H. Rehren, Comm. Math. Phys. 116 (1988) 675.
K.H. Rehren, B. Schroer, Nucl. Phys. B312 (1989) 715.
P. Farlan, A.Ch. Ganchev and V.B. Petkova, Trieste preprint INFN/AE-89/3 (1989), to appear in Int. J. Mod. Phys. A.
V.S. Dotsenko, Kyoto preprint RIMS-559 (1986).
P.P. Kulish, N.Yu. Reshetikhin, Zapiski nauch. semin. LOMI 101 (1980) 112 (in Russian), English transl. J. Sov. Math. 23 (1983) 2435.
V.G. Drinfeld, Doklady AN USSR, 283, no. 5 (1985) 1060.
M. Jimbo, Lett. Math. Phys., 10 (1985) 63, 11 (1986) 247.
E.K. Sklyanin, Funct. Anal. and Appl., 16 (1982) 263.
L.L. Vaksman and Y.S. Soibelmann, Funct. anal. i pril., 22, no. 3 (1988) 1.
H. Batteman, A. Erdelyi, Higher Transcendental Functions, v.I., Mc Graw-Hill, New York (1953).
P. Roche and D. Arnandon, Lett. Math. Phys. 17 (1989) 295.
B.L. Feigin and D.B. Fuks, Fund. anal. i pril. 17, no. 3 (1983) 81.
A.Ch. Ganchev and V.B. Petkova, Trieste preprint IC/89/158 (1989), to appear in Phys. Lett. B.
L. Alvarez-Gaumé, C. Gomez, and G. Sierra, preprint CERN-TH.5369/89 (1989).
S.V. Kerov, Zapiski nauch. semin. LOMI, 161 (1987) 155 (in Russian).
H. Wenzl, Inn. Math. 92 (1988) 349.
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Ganchev, A.C., Petkova, V.B. (1990). U q (sl(2)) Invariant operators and reduced polynomial identities. In: Doebner, H.D., Hennig, J.D. (eds) Quantum Groups. Lecture Notes in Physics, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53503-9_43
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DOI: https://doi.org/10.1007/3-540-53503-9_43
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