Geodesic
Toward a vertex operator construction of quantum affine algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 240-248 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe a construction of the quantum-deformed affine algebras using vertex operators in the free field theory. We prove the Serre relations for the Borel subalgebras of quantum affine algebras; in particular, we consider the $\widehat{sl}_2$ case in detail. We also construct the generators corresponding to the positive roots of $\widehat{sl}_2$.
Keywords: quantum group, quantum affine algebra, free field theory, minimal model
Mots-clés : Serre relations. 
@article{TMF_2008_154_2_a2,
     author = {S. E. Klevtsov},
     title = {Toward a vertex operator construction of quantum affine algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {240--248},
     year = {2008},
     volume = {154},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a2/}
}
TY  - JOUR
AU  - S. E. Klevtsov
TI  - Toward a vertex operator construction of quantum affine algebras
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 240
EP  - 248
VL  - 154
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a2/
LA  - ru
ID  - TMF_2008_154_2_a2
ER  - 
%0 Journal Article
%A S. E. Klevtsov
%T Toward a vertex operator construction of quantum affine algebras
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 240-248
%V 154
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a2/
%G ru
%F TMF_2008_154_2_a2
S. E. Klevtsov. Toward a vertex operator construction of quantum affine algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 240-248. http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a2/

[1] I. Frenkel, V. Kac, Invent. Math., 62 (1980), 23 ; G. Segal, Comm. Math. Phys., 80 (1981), 301 | DOI | MR | Zbl | DOI | MR | Zbl

[2] P. Goddard, D. Olive, Internat. J. Modern Phys. A, 1 (1986), 303 | DOI | MR | Zbl

[3] M. B. Halpern, Phys. Rev. D, 12 (1975), 1684 ; 13 (1976), 337 ; T. Banks, D. Horn, H. Neuberger, Nucl. Phys. B, 108 (1976), 119 | DOI | MR | DOI | MR | DOI

[4] V. Dotsenko, Adv. Stud. Pure Math., 16 (1988), 123 | MR | Zbl

[5] A. Gerasimov, A. Marshakov, A. Morozov, M. Olshanetsky, S. Shatashvili, Internat. J. Modern Phys. A, 5 (1990), 2495 | DOI | MR

[6] G. Felder, Nucl. Phys. B, 317 (1989), 215 | DOI | MR

[7] B. L. Feigin, E. V. Frenkel, UMN, 43:5 (263) (1988), 227 | MR | Zbl

[8] A. Tsuchiya, Y. Kanie, Lett. Math. Phys., 13 (1987), 303 | DOI | MR | Zbl

[9] P. Bouwknegt, J. McCarthy, K. Pilch, Comm. Math. Phys., 131 (1990), 125 | DOI | MR | Zbl

[10] P. Bouwknegt, J. McCarthy, K. Pilch, Progr. Theoret. Phys. Suppl., 102 (1990), 67 | DOI | MR | Zbl

[11] A. Varchenko, V. Schechtman, Integral Representations of $N$-Point Conformal Correlators in the WZW Model, Preprint MPI/89-51, Max-Planck Institute, Bonn, 1989

[12] A. Varchenko, Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups, Adv. Ser. Math. Phys., 21, World Scientific, Singapore, 1995 | DOI | MR | Zbl

[13] B. Feigin, E. Frenkel, “Integrals of motion and quantum groups”, Integrable systems and quantum groups (Montecatini Terme, 1993), Lecture Notes in Math., 1620, Springer, Berlin, 1996, 349 ; arXiv: hep-th/9310022 | DOI | MR | Zbl

[14] O. Babelon, L. Bonora, Phys. Lett. B, 244 (1990), 220 | DOI | MR

[15] V. Dotsenko, V. Fateev, Nucl. Phys. B, 240 (1984), 312 ; 251 (1985), 691 | DOI | MR | DOI | MR