Vertex-IRF transformations and quantization of dynamical r-matrices

Mathematical Research Letters

Volumn 8, Issue 3, 2001, Pages 331-345

  Etingof, Pavel ^a,b   Nikshych, Dmitri ^a,c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b Columbia University ^*  (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035535891     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.2001.v8.n3.a9     Document Type: Article

References (17)

1. [BBB] O. Babelon, D. Bernard, and E. Billey, A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations, Phys. Lett. B 375 (1996), 89-97.
2. [BNSz] G. Böhm, F. Nill, and K. Szlachányi, Weak Hopf algebras I. Integral theory and C*-structure, J. Algebra, 221 (1999), 385-438.
3. [EK] P. Etingof and D. Kazhdan, Quantization of Lie bialgebras. II, Selecta Math. (N.S.) 4 (1998), 213-231.
4. [EN1] P. Etingof, D. Nikshych, Dynamical quantum groups at roots of 1, Duke Math. J., 108 (2001), to appear, math.QA/0003221.
5. [EN2] P. Etingof, D. Nikshych, Dynamical twists in finite groups, Internat. Math. Res. Notices, to appear, math.QA/0101046.
6. [ES1] P. Etingof, O. Schiffmann, A link between two elliptic quantum groups, Asian J. Math. 2 (1998), 345-354.
7. [ES2] _, Lectures on the dynamical Yang-Baxter equations, preprint, math.QA/9908064 (1999).
8. [ES3] _, On the moduli space of classical dynamical r-matrices, preprint, math.QA/0005282 (2000).
9. [EV] P. Etingof, A. Varchenko, Exchange dynamical quantum groups, Comm. Math. Phys. 205 (1999), 19-52.
10. [GGS] M. Gerstenhaber, A. Giaquinto, and S. Schack, Quantum symmetry, in : "Quantum groups" (Leningrad, 1990), 9-46, Lecture Notes in Math. 1510, Springer, Berlin, 1992.
11. [F] G. Felder, Elliptic quantum groups, XIth International Congress of Mathematical Physics (1994), 211-218, Internat. Press, Cambridge, 1995.
12. [Has] K. Hasegawa, L-operator for Belavin's R-matrix acting on the space of theta functions, J. Math. Phys. 35 (1994), 6158-6171.
13. [Ho] T. Hodges, Generating functions for coefficients of Cremmer-Gervais R-matrices, math.QA/9903113.
14. [JOKS] M. Jimbo, S. Odake, H. Konno, and J. Shiraishi, Quasi-Hopf twistors for elliptic quantum groups, Transform. Groups 4 (1999), 303-327.
15. [KZ] I.M. Krichever and A. Zabrodin, Spin generalization of the Ruijsenaars-Schneider model, the nonabelian two-dimensionalized Toda lattice, and representations of the Sklyanin algebra, (Russian) Uspekhi Mat. Nauk 50 (1995), 3-56, translation in Russian Math. Surveys 50 (1995), 1101-1150.
16. [M] S. Majid, Foundations of quantum group theory, Cambridge University Press, 1995.
17. [X] P. Xu, Triangular dynamical r-matrices and quantization, preprint, math.QA/0005006.