Geodesic
Factorization of the universal $\mathcal R $-matrix for ${U_q(\widehat{sl}_2)} $
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 179-214 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The factorization of the universal $\mathcal R$-matrix corresponding to the so-called Drinfeld Hopf structure is described in the example of the quantum affine algebra $U_q(\widehat{sl}_2)$. As a result of the factorization procedure, we deduce certain differential equations on the factors of the universal $\mathcal R$-matrix that allow uniquely constructing these factors in the integral form. 
@article{TMF_2000_124_2_a0,
     author = {J. Ding and S. Z. Pakulyak and S. M. Khoroshkin},
     title = {Factorization of the universal $\mathcal R $-matrix for ${U_q(\widehat{sl}_2)} $},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--214},
     year = {2000},
     volume = {124},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a0/}
}
TY  - JOUR
AU  - J. Ding
AU  - S. Z. Pakulyak
AU  - S. M. Khoroshkin
TI  - Factorization of the universal $\mathcal R $-matrix for ${U_q(\widehat{sl}_2)} $
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2000
SP  - 179
EP  - 214
VL  - 124
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a0/
LA  - ru
ID  - TMF_2000_124_2_a0
ER  - 
%0 Journal Article
%A J. Ding
%A S. Z. Pakulyak
%A S. M. Khoroshkin
%T Factorization of the universal $\mathcal R $-matrix for ${U_q(\widehat{sl}_2)} $
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2000
%P 179-214
%V 124
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a0/
%G ru
%F TMF_2000_124_2_a0
J. Ding; S. Z. Pakulyak; S. M. Khoroshkin. Factorization of the universal $\mathcal R $-matrix for ${U_q(\widehat{sl}_2)} $. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 179-214. http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a0/

[1] L. A. Takhtadzhan, L. D. Faddeev, UMN, 34:5 (1979), 13–63 | MR

[2] V. G. Drinfeld, DAN SSSR, 286:1 (1987), 13–17

[3] M. Jimbo, Lett. Math. Phys., 10 (1985), 63–69 ; Commun. Math. Phys., 102 (1986), 537–547 | DOI | MR | Zbl | DOI | MR | Zbl

[4] C. Frønsdal, Lett. Math. Phys., 40 (1997), 117–134 | DOI | MR

[5] D. Arnaudon, E. Buffenoir, E. Ragoucy, Ph. Roche, Lett. Math. Phys., 44 (1998), 201 | DOI | MR | Zbl

[6] M. Jimbo, H. Konno, S. Odake, J. Shiraishi, Elliptic algebra $U_{q,p}(\widehat{sl}_2)$: Drinfeld currents and vertex operators, E-print math.QA/9802002 | MR

[7] G. Andrews, R. Baxter, J. Forrester, J. Stat. Phys., 35 (1984), 193–266 | DOI | MR | Zbl

[8] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR

[9] A. Zamolodchikov, Al. Zamolodchikov, Ann. Phys. (N. Y), 120 (1979), 253–291 | DOI | MR

[10] V. G. Drinfeld, Algebra i analiz, 1:6 (1989), 114–148 | MR

[11] V. G. Drinfeld, “Quantum groups”, Proc. Int. Congr. Math., V. 1 (Berkley, Ca, 1986), ed. A. M. Cleason, Amer. Math. Soc., Providence, 1987, 798–820 | MR

[12] S. Khoroshkin, V. Tolstoy, Twisting of quantum (super)algebras. Connection of Drinfeld's and Cartan–Weyl realizations for quantum affine algebras, Preprint MPI/94-23, Max Plank Institut, Bonn, 1994 ; E-print hep-th/9404036 | MR

[13] B. Enriquez, G. Felder, Elliptic quantum groups $E_{\tau,\eta}(\widehat{sl}_2)$ and quasi-Hopf algebras, E-print q-alg/9703018 | MR

[14] B. Enriquez, V. Rubtsov, Quasi-Hopf algebras associated with $\frak{sl}(2)$ and complex curves, E-print q-alg/9608005 | MR

[15] J. Ding, S. Khoroshkin, Weyl group extension of quantized current algebras, E-print math.QA/9804139 | MR

[16] J. Ding, S. Khoroshkin, S. Pakuliak, Integral representations for universal $\mathcal R$-matrix, Preprint ITEP-TH-67/99, ITEP, M., 1999 ; http://wwwth.itep.ru/mathphys/psfiles/99_67.ps | MR

[17] S. Khoroshkin, D. Lebedev, S. Pakuliak, Commun. Math. Phys., 190 (1998), 597–627 | DOI | MR | Zbl

[18] J. Beck, Commun. Math. Phys., 165 (1994), 555–568 | DOI | MR | Zbl

[19] S. Khoroshkin, V. Tolstoy, J. Geom. Phys., 11 (1993), 101–108 | DOI | MR

[20] I. Damiani, J. Algebra, 161 (1993), 291–310 | DOI | MR | Zbl

[21] J. Ding, T. Miwa, Zeros and poles of quantum current operators and the condition of quantum integrability, E-print q-alg/9608001 | MR

[22] V. N. Tolstoi, S. M. Khoroshkin, Funkts. analiz i ego prilozh., 26:1 (1992), 85–88 | MR | Zbl

[23] I. Makdonald, Simmetricheskie funktsii i mnogochleny Kholla, Mir, M., 1985 | MR

[24] I. Cherednik, Invent. Math., 122 (1995), 119–145 | DOI | MR | Zbl

[25] S. Khoroshkin, V. Tolstoy, A. Stolin, Mod. Phys. Lett. A, 10:19 (1995), 1375–1392 | DOI | MR | Zbl