Yangian Double

Letters in Mathematical Physics

Volumn 36, Issue 4, 1996, Pages 373-402

  Khoroshkin, S M ^a   Tolstoy, V N ^b  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Quantum affine algebra; Universal enveloping algebra; Yang baxter equation; Yangian double

Indexed keywords

EID: 0001584896     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00714404     Document Type: Article

References (27)

1. Bernard, D. and LeClair, A., The quantum double in Integrable quantum field theory, Preprint CLNS 92/1147 (1992).
2. Chari, V. and Pressley, A., Yangians and R-matrices, Enseign. Math. 36, 267-302 (1990).
3. Chari, V. and Pressley, A., Fundamental representations of Yangians and singulariries of R-matrices. J. Reine Angew. Math. 417, 87-128 (1991).
4. Cherednik, I. V., A new interpretation of Gelfand-Zetlin bases, Duke Math. J. 54, 563-577 (1987).
5. Drinfeld, V. G., Hopf algebras and quantum Yang-Baxter equation. Soviet Math. Dokl. 28, 1060-1064 (1985).
6. Drinfeld, V. G., A new realization of Yangians and quantized affine algebras, Soviet Math. Dokl. 32, 212-216 (1988).
7. Drinfeld, V. G., A new realization of Yangians and quantized affine algebras, Preprint FTINT 30-86 (1986).
8. Drinfeld, V. G., Quantum groups, in Proc. ICM-86 (Berkeley USA) vol. 1, Amer. Math. Soc. Providence, RI, 1987, pp. 798-820.
9. Drinfeld, V. G., Private communication.
10. q(gl(n)), Comm. Math. Phys. 156, 277-300 (1993).
11. Faddeev, L. D., Reshetikhin, N. Yu., and Takhtajan, L. A., quantization of Lie groups and Lie algebras, Algebra Anal. 1, 178-201 (1989).
12. Frenkel, I. B. and Reshetikhin, N. Yu., Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146, 1-60 (1992).
13. Jimbo, M., A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10, 63-69 (1985).
14. Khoroshkin, S. M., Stolin, A. A., and Tolstoy, V. N., Generalized Gauss decomposition of trigonometric R-matrices. Preprint TRITA-MAT-1994-0041 (Nov. 1994), hep-th 9404038.
15. Khoroshkin, S. M. and Tolstoy, V. N., Universal R-matrix for quantized (super) algebras, Comm. Math. Phys. 141, 599-617 (1991).
16. Khoroshkin, S. M. and Tolstoy, V. N., The universal R-matrix for quantum nontwisted affine Lie algebras, Funktsional. Anal. i Prilozhen 26, 85-88 (1992).
17. Khoroshkin, S. M. and Tolstoy, V. N., The Cartan-Weyl basis and the universal R-matrix for quantum Kac-Moody algebras and superalgebras, in: H. Doebner and V. Dobrev (eds), Quantum Symmetries, World Scientific, Singapore, 1993.
18. Khoroshkin, S. M. and Tolstoy, V. N., Twisting of quantum (super)algebras. Connection of Drinfeld's and Cartan-Weyl realizations for quantum affine superalgebras. Preprint MPIM-Bonn, MPI 94/23 (1993), hep/th 9404036.
19. Molev, A. I., Private communication.
20. Nazarov, M. and Tarasov, V., Yangians and Gelfand-Zetlin bases, RIMS preprint (1992).
21. Olshanskii, G., Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians. in: A. A. Kirillov (ed), Topics in Representation Theory, Adv. Sov. Math. 2, AMS, Providence, RI, 1991, pp. 1-66.
22. Reshetikhin, N. Yu and Semenov-Tyan-Shansky, M. A., Central extensions of quantum current groups, Lett. Math. Phys. 19, 133-142 (1990).
23. a(sl(n + 1)), Comm, Math. Phys. 124, 307-318 (1989).
24. Smirnov, F. A., Dynamical symmetries of massive integrable models, J. Modern Phys. A, 7 suppl. 1B, 813-838 (1992).
25. Tarasov, V. O., On the structure of quantum L-operator for the L-matrix of the XXZ-model. Teoret. Mat. Fiz. 61, 163-173 (1984) (Russian).
26. Tarasov, V. O., Irreducible monodromy matrices of the XXZ-model and lattice local quantum Hamiltonians, Teoret. Mat. Fiz. 63, 175-196 (1985) (Russian).
27. Tolstoy, V. N., Extremal projectors for contragredient Lie algebras and superalgebras of finite growth, Uspekhi Math. Nauk 44, 211-212 (1989).