Level one representations of $U_q(G_2^{(1)}$
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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
- A. Abada, A. H. Bougourzi, and M. A. El Gradechi, Deformation of the Wakimoto construction, Modern Phys. Lett. A 8 (1993), no. 8, 715–723. MR 1213839, DOI 10.1142/S0217732393000738
- Hidetoshi Awata, Satoru Odake, and Jun’ichi Shiraishi, Free boson realization of $U_q(\widehat {\textrm {sl}_N})$, Comm. Math. Phys. 162 (1994), no. 1, 61–83. MR 1272767
- Jonathan Beck, Braid group action and quantum affine algebras, Comm. Math. Phys. 165 (1994), no. 3, 555–568. MR 1301623
- Denis Bernard, Vertex operator representations of the quantum affine algebra $\scr U_q(B^{(1)}_r)$, Lett. Math. Phys. 17 (1989), no. 3, 239–245. MR 995803, DOI 10.1007/BF00401590
- Denis Bernard and Jean Thierry-Mieg, Level one representations of the simple affine Kac-Moody algebras in their homogeneous gradations, Comm. Math. Phys. 111 (1987), no. 2, 181–246. MR 899850
- V. G. Drinfel′d, A new realization of Yangians and of quantum affine algebras, Dokl. Akad. Nauk SSSR 296 (1987), no. 1, 13–17 (Russian); English transl., Soviet Math. Dokl. 36 (1988), no. 2, 212–216. MR 914215
- Igor B. Frenkel and Nai Huan Jing, Vertex representations of quantum affine algebras, Proc. Nat. Acad. Sci. U.S.A. 85 (1988), no. 24, 9373–9377. MR 973376, DOI 10.1073/pnas.85.24.9373
- I. B. Frenkel and N. Yu. Reshetikhin, Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146 (1992), no. 1, 1–60. MR 1163666
- P. Goddard, W. Nahm, D. Olive, and A. Schwimmer, Vertex operators for non-simply-laced algebras, Comm. Math. Phys. 107 (1986), no. 2, 179–212. MR 863639
- Takahiro Hayashi, $q$-analogues of Clifford and Weyl algebras—spinor and oscillator representations of quantum enveloping algebras, Comm. Math. Phys. 127 (1990), no. 1, 129–144. MR 1036118
- Michio Jimbo and Tetsuji Miwa, Algebraic analysis of solvable lattice models, CBMS Regional Conference Series in Mathematics, vol. 85, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1995. MR 1308712
- Nai Huan Jing, Twisted vertex representations of quantum affine algebras, Invent. Math. 102 (1990), no. 3, 663–690. MR 1074490, DOI 10.1007/BF01233443
- Naihuan Jing, Higher level representations of the quantum affine algebra $U_q(\widehat \textrm {sl}(2))$, J. Algebra 182 (1996), no. 2, 448–468. MR 1391593, DOI 10.1006/jabr.1996.0180
- 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.
- N. Jing, Quantum $Z$-algebras and representations of quantum affine algebras, to appear.
- N. Jing, Y. Koyama, and K. C. Misra, Bosonic realizations of $U_q(C_n^{(1)})$, J. Algebra, to appear; q-alg/9701035.
- N. Jing, Y. Koyama, and K. C. Misra, Level one realizations of quantum affine algebras $U_q(C_n^{(1)})$, to appear.
- James Lepowsky and Mirko Primc, Standard modules for type one affine Lie algebras, Number theory (New York, 1982) Lecture Notes in Math., vol. 1052, Springer, Berlin, 1984, pp. 194–251. MR 750666, DOI 10.1007/BFb0071544
- James Lepowsky and Robert Lee Wilson, A new family of algebras underlying the Rogers-Ramanujan identities and generalizations, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 12, 7254–7258. MR 638674, DOI 10.1073/pnas.78.12.7254
- G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70 (1988), no. 2, 237–249. MR 954661, DOI 10.1016/0001-8708(88)90056-4
- Atsushi Matsuo, A $q$-deformation of Wakimoto modules, primary fields and screening operators, Comm. Math. Phys. 160 (1994), no. 1, 33–48. MR 1262190
- Jun’ichi Shiraishi, Free boson representation of $U_q(\widehat \textrm {sl}_2)$, Phys. Lett. A 171 (1992), no. 5-6, 243–248. MR 1196422, DOI 10.1016/0375-9601(92)90635-Y
- Yi Chao Xu and Cui Po Jiang, Vertex operators of $G^{(1)}_2$ and $B^{(1)}_l$, J. Phys. A 23 (1990), no. 14, 3105–3121. MR 1063010
Additional Information
- Naihuan Jing
- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
- MR Author ID: 232836
- Email: jing@eos.ncsu.edu
- Received by editor(s): April 30, 1997
- Additional Notes: This research was supported in part by NSA grants MDA904-96-1-0087 and MDA904-97-1-0062.
- Communicated by: Roe Goodman
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 21-27
- MSC (1991): Primary 17B37, 17B67
- DOI: https://doi.org/10.1090/S0002-9939-99-04740-1
- MathSciNet review: 1487318