Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Level one representations of $U_q(G_2^{(1)})$

Author(s): Naihuan Jing
Journal: Proc. Amer. Math. Soc. 127 (1999), 21-27.
MSC (1991): Primary 17B37, 17B67
MathSciNet review: 1487318
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Abstract: We construct a level one representation of the quantum affine algebra $U_q(G_2^{(1)})$ by vertex operators from bosonic fields.

References:

1.: A. Abada, H. Bougourzi and M. El Gradechi, Deformations of Wakimoto representations, Mod. Phys. Lett. A8 (1993), 515-724. MR 94c:81065
2.: H. Awata, S. Odake, and J. Shiraishi, Free boson representation of $U_q(\hat{sl}_N)$ , Commun. Math. Phys. (1994), 61-83. MR 95g:81072
3.: J. Beck, Braid group action and quantum affine algebras, Commun. Math. Phys. 165 (1994), 555-568. MR 95i:17011
4.: D. Bernard, Vertex operator representations of quantum affine algebras $U_q(B^{(1)}_r)$ , Lett. Math. Phys. 17 (1989), 239-245. MR 90f:17016
5.: D. Bernard and J. Thierry-Mieg, Level one representations od the simple affine Kac-Moody algebras in their homogeneous gradations, Commun. Math. Phys. 111 (1987), 181-246. MR 88m:17016
6.: V. G. Drinfeld, A new realization of Yangians and quantized affine algebras , Soviet Math. Dokl., 36 (1988), 212-216. MR 88j:17020
7.: I. B. Frenkel and N. Jing, Vertex representations of quantum affine algebras , Proc. Nat'l. Acad. Sci. USA 85 (1988) , 9373-9377. MR 90e:17028
8.: I. Frenkel and Y. Reshetikhin, Quantum affine algebras and holomorphic difference equations, Commun. Math. Phys. 146, 1-60. MR 94c:17024
9.: P. Goddard, W. Nahm, D. I. Olive, and A. Schwimmer, Vertex operators for non-simply laced algebras, Commun. Math. Phys., 107 (1986), 179-212. MR 87k:17022
10.: H. Hayashi, Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum affine algebras, Commun. Math. Phys. 127 (1990), 129-144. MR 91a:17015
11.: M. Jimbo and T. Miwa, Algebraic analysis of solvable lattice models, CBMS series 85, Amer. Math. Soc., Providence, RI, 1995. MR 96e:82037
12.: N. Jing, Twisted vertex representations of quantum affine algebras, Invent. Math. 102 (1990), 663-690. MR 92a:17019
13.: N. Jing, Higher level representations of the quantum affine algebra $U_q(\widehat{sl}(2))$ , J. Algebra, 182 (1996), 448-468. MR 97f:17017
14.: N. Jing, On Drinfeld realization of quantum affine algebras, in Proc. of Conf. on the Monster and Lie Algebras (May, 1996), eds. by J. Ferrar and K. Harada, de Gruyter Verlag, Berlin, 1997, to appear; q-alg/9610035.
15.: N. Jing, Quantum $Z$ -algebras and representations of quantum affine algebras, to appear.
16.: N. Jing, Y. Koyama, and K. C. Misra, Bosonic realizations of $U_q(C_n^{(1)})$ , J. Algebra, to appear; q-alg/9701035.
17.: N. Jing, Y. Koyama, and K. C. Misra, Level one realizations of quantum affine algebras $U_q(C_n^{(1)})$ , to appear.
18.: J. Lepowsky and M. Primc, Standard modules for type one affine Lie algebras, Lect. Notes in Math., 1052, Springer-Verlag, New York, 1984, pp. 194-251. MR 86f:17015
19.: J. Lepowsky and R. L. Wilson, A new family of algebras underlying the Rogers-Ramanujan identities and generalizations, Proc. Nat'l. Acad. Sci. USA, 78 (1981), 7254-7258. MR 82k:10016
20.: G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. Math. 70 (1988), 237-249. MR 89k:17029
21.: A. Matsuo, A $q$ -deformation of Wakimoto modules, primary fields and screening operators, Commun.Math.Phys. 160 (1994) 33-48. MR 95h:17033
22.: J. Shiraishi, Free boson representations $U_q(\widehat{sl}_2)$ , Phys. Lett. A171 (1992), 243-248. MR 93k:81108
23.: Y. Xu and C. Jiang, Vertex operators of $G_2^{(1)}$ and $B_l^{(1)}$ , J. Phys. A: Gen. Math. 23 (1990), 3105-3121. MR 91j:17039

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