Geodesic
Three realizations of the quantum affine algebra $U_q(A_2^{(2)})$
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 2, pp. 217-232 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We establish explicit isomorphisms between three realizations of the quantum twisted affine algebra $U_q(A_2^{(2)})$: the Drinfeld current realization, the Chevalley realization, and the so-called $RLL$ realization proposed by Reshetikhin, Takhtajan, and Faddeev.
Keywords: quantum affine algebra, $RLL$ realization. 
@article{TMF_2010_165_2_a1,
     author = {A. M. Shapiro},
     title = {Three realizations of the~quantum affine algebra~$U_q(A_2^{(2)})$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {217--232},
     year = {2010},
     volume = {165},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_165_2_a1/}
}
TY  - JOUR
AU  - A. M. Shapiro
TI  - Three realizations of the quantum affine algebra $U_q(A_2^{(2)})$
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 217
EP  - 232
VL  - 165
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_165_2_a1/
LA  - ru
ID  - TMF_2010_165_2_a1
ER  - 
%0 Journal Article
%A A. M. Shapiro
%T Three realizations of the quantum affine algebra $U_q(A_2^{(2)})$
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 217-232
%V 165
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2010_165_2_a1/
%G ru
%F TMF_2010_165_2_a1
A. M. Shapiro. Three realizations of the quantum affine algebra $U_q(A_2^{(2)})$. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 2, pp. 217-232. http://geodesic.mathdoc.fr/item/TMF_2010_165_2_a1/

[1] A. Izergin, V. Korepin, Comm. Math. Phys., 79:3 (1981), 303–316 | DOI | MR

[2] M. Jimbo, Comm. Math. Phys., 102:4 (1986), 537–547 | DOI | MR | Zbl

[3] V. O. Tarasov, TMF, 76:2 (1988), 184–198 | DOI | MR

[4] D. Fioravanti, F. Ravanini, M. Stanishkov, Phys. Lett. B, 367:1–4 (1996), 113–120, arXiv: hep-th/9510047 | DOI | MR | Zbl

[5] S. M. Khoroshkin, V. N. Tolstoy, Lett. Math. Phys., 24:3 (1992), 231–244 | DOI | MR | Zbl

[6] V. Chari, A. Pressley, Comm. Math. Phys., 196:2 (1998), 461–476 | DOI | MR | Zbl

[7] J. Ding, S. M. Khoroshkin, Adv. Math., 189:2 (2004), 413–438 | DOI | MR | Zbl

[8] S. Khoroshkin, A. Shapiro, J. Geom. and Phys., 60:11 (2010), 1833–1851 | DOI | MR

[9] V. G. Drinfeld, Dokl. AN SSSR, 296:1 (1987), 13–17 | MR

[10] N. Yu. Reshetikhin, L. A. Takhtadzhyan, L. D. Faddeev, Algebra i analiz, 1:1 (1989), 178–206 | MR | Zbl

[11] N. Yu. Reshetikhin, M. A. Semenov-Tian-Shansky, Lett. Math. Phys., 19:2 (1990), 133–142 | DOI | MR | Zbl

[12] J. T. Ding, I. B. Frenkel, Comm. Math. Phys., 156:2 (1993), 277–300 | DOI | MR | Zbl

[13] J. Ding, S. Khoroshkin, Lett. Math. Phys., 45:4 (1998), 331–352 | DOI | MR | Zbl

[14] W.-L. Yang, Y.-Z. Zhang, J. Phys. A, 34:13 (2001), L205–L211 | DOI | MR | Zbl

[15] D. Hernandez, Int. Math. Res. Not., 2010:1 (2010), 149–193, arXiv: 0704.2838 | MR | Zbl

[16] J. Ding, S. Khoroshkin, Transform. Groups, 5:1 (2000), 35–59 | DOI | MR | Zbl

[17] S. Khoroshkin, S. Pakuliak, J. Math. Kyoto Univ., 48:2 (2008), 277–321 | DOI | MR | Zbl

[18] B. Enriquez, S. Khoroshkin, S. Pakuliak, Comm. Math. Phys., 276:3 (2007), 691–725 | DOI | MR | Zbl