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| 1. |
Asherova R. M., Smirnov Yu. F., Tolstoy V. N., “Description of a class of projection operators for semisimple complex Lie algebras”, Math. Notes, 26 (1979), 499–504 |
| 2. |
Bazhanov V. V., Hibberd A. N., Khoroshkin S. M., “Integrable structure of ${\mathcal W}_3$ conformal field theory, quantum Boussinesq theory and boundary affine Toda theory”, Nuclear Phys. B, 622 (2002), 475–547, arXiv: hep-th/0105177 |
| 3. |
Bazhanov V. V., Lukyanov S. L., Zamolodchikov A. B., “Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz”, Comm. Math. Phys., 177 (1996), 381–398, arXiv: hep-th/9412229 |
| 4. |
Bazhanov V. V., Lukyanov S. L., Zamolodchikov A. B., “Integrable structure of conformal field theory. II. ${\rm Q}$-operator and DDV equation”, Comm. Math. Phys., 190 (1997), 247–278, arXiv: hep-th/9604044 |
| 5. |
Bazhanov V. V., Lukyanov S. L., Zamolodchikov A. B., “Integrable structure of conformal field theory. III. The Yang–Baxter relation”, Comm. Math. Phys., 200 (1999), 297–324, arXiv: hep-th/9805008 |
| 6. |
Beck J., “Braid group action and quantum affine algebras”, Comm. Math. Phys., 165 (1994), 555–568, arXiv: hep-th/9404165 |
| 7. |
Boos H., Göhmann F., Klümper A., Nirov Kh. S., Razumov A. V., “Exercises with the universal $R$-matrix”, J. Phys. A: Math. Theor., 43 (2010), 415208, 35 pp., arXiv: 1004.5342 |
| 8. |
Boos H., Göhmann F., Klümper A., Nirov Kh.S., Razumov A. V., “Universal integrability objects”, Theoret. and Math. Phys., 174 (2013), 21–39, arXiv: 1205.4399 |
| 9. |
Boos H., Göhmann F., Klümper A., Nirov Kh.S., Razumov A. V., “Quantum groups and functional relations for higher rank”, J. Phys. A: Math. Theor., 47 (2014), 275201, 47 pp., arXiv: 1312.2484 |
| 10. |
Boos H., Göhmann F., Klümper A., Nirov Kh. S., Razumov A. V., “Universal $R$-matrix and functional relations”, Rev. Math. Phys., 26 (2014), 1430005, 66 pp., arXiv: 1205.1631 |
| 11. |
Boos H., Göhmann F., Klümper A., Nirov Kh. S., Razumov A. V., “Oscillator versus prefundamental representations”, J. Math. Phys., 57 (2016), 111702, 23 pp., arXiv: 1512.04446 |
| 12. |
Boos H., Göhmann F., Klümper A., Nirov Kh. S., Razumov A. V., Oscillator versus prefundamental representations. II. Arbitrary higher ranks, arXiv: 1701.0262 |
| 13. |
Chari V., Pressley A., “Quantum affine algebras”, Comm. Math. Phys., 142 (1991), 261–283 |
| 14. |
Chari V., Pressley A., A guide to quantum groups, Cambridge University Press, Cambridge, 1994 |
| 15. |
Damiani I., “Drinfeld realization of affine quantum algebras: the relations”, Publ. Res. Inst. Math. Sci., 48 (2012), 661–733, arXiv: 1406.6729 |
| 16. |
Damiani I., “From the Drinfeld realization to the Drinfeld–Jimbo presentation of affine quantum algebras: injectivity”, Publ. Res. Inst. Math. Sci., 51 (2015), 131–171, arXiv: 1407.0341 |
| 17. |
Drinfel'd V. G., “Hopf algebras and the quantum Yang–Baxter equation”, Sov. Math. Dokl., 32 (1985), 254–258 |
| 18. |
Drinfel'd V. G., “Quantum groups”, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), v. 1, 2, Amer. Math. Soc., Providence, RI, 1987, 798–820 |
| 19. |
Drinfel'd V. G., “A new realization of Yangians and of quantum affine algebras”, Sov. Math. Dokl., 36 (1988), 212–216 |
| 20. |
Etingof P. I., Frenkel I. B., Kirillov Jr. A.A., Lectures on representation theory and Knizhnik–Zamolodchikov equations, Mathematical Surveys and Monographs, 58, Amer. Math. Soc., Providence, RI, 1998 |
| 21. |
Feigin B., Jimbo M., Miwa T., Mukhin E., Finite type modules and Bethe ansatz equations, arXiv: 1609.05724 |
| 22. |
Frenkel E., Hernandez D., “Baxter's relations and spectra of quantum integrable models”, Duke Math. J., 164 (2015), 2407–2460, arXiv: 1308.3444 |
| 23. |
Frenkel E., Reshetikhin N., “The $q$-characters of representations of quantum affine algebras and deformations of $\mathcal W$-algebras”, Recent Developments in Quantum Affine Algebras and Related Topics (Raleigh, NC, 1998), Contemp. Math., 248, Amer. Math. Soc., Providence, RI, 1999, 163–205, arXiv: math.QA/9810055 |
| 24. |
Hernandez D., “Representations of quantum affinizations and fusion product”, Transform. Groups, 10 (2005), 163–200, arXiv: math.QA/0312336 |
| 25. |
Hernandez D., “Drinfeld coproduct, quantum fusion tensor category and applications”, Proc. Lond. Math. Soc., 95 (2007), 567–608, arXiv: math.QA/0504269 |
| 26. |
Hernandez D., Jimbo M., “Asymptotic representations and Drinfeld rational fractions”, Compos. Math., 148 (2012), 1593–1623, arXiv: 1104.1891 |
| 27. |
Jimbo M., “A $q$-difference analogue of $U({\mathfrak g})$ and the Yang–Baxter equation”, Lett. Math. Phys., 10 (1985), 63–69 |
| 28. |
Jimbo M., “A $q$-analogue of $U({\mathfrak g}{\mathfrak l}(N+1))$, Hecke algebra, and the Yang–Baxter equation”, Lett. Math. Phys., 11 (1986), 247–252 |
| 29. |
Jimbo M., Miwa T., Algebraic analysis of solvable lattice models, CBMS Regional Conference Series in Mathematics, 85, Amer. Math. Soc., Providence, RI, 1995 |
| 30. |
Kac V. G., Infinite-dimensional Lie algebras, 3rd ed., Cambridge University Press, Cambridge, 1990 |
| 31. |
Khoroshkin S. M., Tolstoy V. N., “On Drinfel'd's realization of quantum affine algebras”, J. Geom. Phys., 11 (1993), 445–452 |
| 32. |
Khoroshkin S. M., Tolstoy V. N., Twisting of quantum (super)algebras. Connection of Drinfeld's and Cartan–Weyl realizations for quantum affine algebras, arXiv: hep-th/9404036 |
| 33. |
Leznov A. N., Savel'ev M. V., “A parametrization of compact groups”, Funct. Anal. Appl., 8 (1974), 347–348 |
| 34. |
Meneghelli C., Teschner J., Integrable light-cone lattice discretizations from the universal ${R}$-matrix, arXiv: 1504.04572 |
| 35. |
Mukhin E., Young C. A. S., Trans. Amer. Math. Soc., 366 (2014), Affinization of category $\mathcal{O}$ for quantum groups, arXiv: 1204.2769 |
| 36. |
Nirov Kh. S., Razumov A. V., “Quantum groups and functional relations for lower rank”, J. Geom. Phys., 112 (2017), 1–28, arXiv: 1412.7342 |
| 37. |
Nirov Kh. S., Razumov A. V., Quantum groups, {V}erma modules and $q$-oscillators: General linear case, arXiv: 1610.02901 |
| 38. |
Razumov A. V., “Monodromy operators for higher rank”, J. Phys. A: Math. Theor., 46 (2013), 385201, 24 pp., arXiv: 1211.3590 |
| 39. |
Tolstoy V. N., Khoroshkin S. M., “The universal $R$-matrix for quantum untwisted affine Lie algebras”, Funct. Anal. Appl., 26 (1992), 69–71 |
| 40. |
Yamane H., “A Poincaré–Birkhoff–Witt theorem for quantized universal enveloping algebras of type $A_N$”, Publ. Res. Inst. Math. Sci., 25 (1989), 503–520 |