Volkov pentagon for the modular quantum dilogarithm
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 65-71.

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The new form of pentagon equations suggested by Volkov (Int. Math. Res. Notices (2011); http://arxiv.org/abs/1104.2267) for the $q$-exponential on the basis of formal series is derived within the Hilbert space framework for the modular version of the quantum dilogarithm.
Mots-clés : pentagon equations
Keywords: $q$-exponential, quantum dilogarithm.
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L. D. Faddeev. Volkov pentagon for the modular quantum dilogarithm. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 65-71. http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a5/

[1] A. Yu. Volkov, “Pentagon identity revisited”, Int. Math. Res. Notices, 2011 ; arXiv: 1104.2267 | DOI | MR

[2] M. P. Schützenberger, “Une interprétation de certaines solutions de l'équation fonctionnelle $F(x+y)=F(x)F(y)$”, C. R. Acad. Sci. Paris, 236 (1953), 352–353 | MR | Zbl

[3] L. D. Faddeev, A. Y. Volkov, “Abelian current algebra and the Virasoro algebra on the lattice”, Phys. Lett. B, 315 (1993), 311–318 ; arXiv: hep-th/9307048 | DOI | MR | Zbl

[4] L. D. Faddeev, R. M. Kashaev, “Quantum dilogarithm”, Modern. Phys. Lett. A, 9:5 (1994), 427–434 ; arXiv: hep-th/9310070 | DOI | MR | Zbl

[5] R. Kashaev, T. Nakanishi, Classical and quantum dilogarithm identities, arXiv: 1104.4630

[6] L. D. Faddeev, “Discrete Heisenberg–Weyl group and modular group”, Lett. Math. Phys., 34:3 (1995), 249–254 | DOI | MR | Zbl

[7] L. D. Faddeev, “Modular double of quantum group”, Math. Phys. Stud., 21 (2000), 149–156 ; arXiv: math/9912078 | MR | Zbl

[8] A. Yu. Volkov, Noncommutative hypergeometry, arXiv: math/0312084

[9] E. W. Barnes, “The genesis of the double gamma function”, Proc. London Math. Soc., 31 (1899), 358–381 | DOI | MR | Zbl

[10] R. M. Kashaev, Liouville central charge in quantum Teichmüller theory, arXiv: hep-th/9811203

[11] R. M. Kashaev, “Quantization of Teichmueller spaces and the quantum dilogarithm”, Lett. Math. Phys., 43:2 (1998), 105–115 | DOI | MR | Zbl

[12] V. G. Drinfeld, “Kvantovye gruppy”, Zap. nauchn. semin. LOMI, 155, 1986, 19–49

[13] L. Faddeev, A. Yu. Volkov, “Hirota equation as an example of integrable symplectic map”, Lett. Math. Phys., 32:2 (1994), 125–135 ; arXiv: hep-th/9405087 | DOI | MR | Zbl

[14] L. D. Faddeev, R. M. Kashaev, A. Y. Volkov, “Strongly coupled quantum discrete Liouville theory. 1. Algebraic approach and duality”, Comm. Math. Phys., 219:1 (2001), 199–219 ; arXiv: hep-th/0006156 | DOI | MR | Zbl

[15] B. Ponsot, J. Teschner, “Clebsch–Gordan and Racah–Wigner coefficients for a continuous series of representations of $U_{q}(sl(2,R))$”, Comm. Math. Phys., 224:3 (2001), 613–655 ; arXiv: math.QA/0007097 | DOI | MR

[16] A. Yu. Volkov, L. D. Faddeev, “Kvantovyi metod obratnoi zadachi na diskretnom prostranstve-vremeni”, TMF, 92:2 (1992), 207–214 ; Preprint HU-TFT-93-30 | MR

[17] L. Chekhov, V. Fock, Quantum Teichmüller spaces, arXiv: math.QA/9908165

[18] A. B. Goncharov, The pentagon relation for the quantum dilogarithm and quantized $M_{0,5}$, arXiv: 0706.4054v2