Available in electronic format
Available in print format
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

Vertex operators for twisted quantum affine algebras

Author(s): Naihuan Jing; Kailash C. Misra
Journal: Trans. Amer. Math. Soc. 351 (1999), 1663-1690.
MSC (1991): Primary 17B37, 17B67; Secondary 82B23, 81R10, 81R50
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We construct explicitly the $q$-vertex operators (intertwining operators) for the level one modules $V(\Lambda _i)$ of the classical quantum affine algebras of twisted types using interacting bosons, where $i=0, 1$ for $A_{2n-1}^{(2)}$ ($n\geq 3$), $i=0$ for $D_4^{(3)}$, $i=0, n$ for $D_{n+1}^{(2)}$ ($n\geq 2$), and $i=n$ for $A_{2n}^{(2)}$ ($n\geq 1$). A perfect crystal graph for $D_4^{(3)}$ is constructed as a by-product.


References:

1.
B. Davies, O. Foda, M. Jimbo, T. Miwa and A. Nakayashiki, Diagonalization of the XXZ Hamiltonian by vertex operators, Commun. Math. Phys. 151 (1993), 89-153. MR 94a:82018

2.
E. Date, M. Jimbo, and M. Okado, Crystal base and $q$-vertex operators, Commun. Math. Phys. 155 (1993), 47-69. MR 94f:17012

3.
V.G. Drinfeld, A new realization of Yangians and quantized affine algebras, Soviet Math. Dokl. 36 (1988), 212-216. MR 88j:17020

4.
I.B. Frenkel and N. Jing, Vertex representations of quantum affine algebras, Proc. Natl. Acad. Sci. USA 85 (1988), 9373-9377. MR 90e:17028

5.
I.B. Frenkel and N. Reshetikhin, Quantum affine algebras and holonomic difference equations, Commun. Math. Phys. 146 (1992), 1-60. MR 94c:17024

6.
M. Idzumi, Level two irreducible representations of $U_q(\hat{sl}_2)$, Int. J. Mod. Phys. A. 9 (1994), 4449-4484. MR 95j:17029

7.
M. Jimbo, K. Miki, T.Miwa and A. Nakayashiki, Correlation functions of the XXZ model for $\Delta < -1$, Phys. Lett. A 168 (1992), 256-263. MR 93m:82007

8.
M. Jimbo and T. Miwa, Algebraic analysis of solvable lattice models, CBMS series 85, Amer. Math. Soc., Providence, RI, 1995. MR 96e:82037

9.
N. Jing, Twisted vertex representations of quantum affine algebras, Invent. Math. 102 (1990), 663-690. MR 92a:17019

10.
N. Jing, Higher level representations of the quantum affine algebra $U_q(\hat{sl}(2))$, J. Algebra 182 (1996), 448-468. MR 97f:17017

11.
N. Jing, On Drinfeld realization of quantum affine algebras, in The Monster and Lie Algebras, ed. J. Ferrar and K. Harada, Ohio State Univ. Math. Res. Publ. 7, de Gruyter, Berlin-New York, 1998. q-alg/9610035.

12.
N. Jing, S.-J. Kang, Y. Koyama, Vertex operators of quantum affine Lie algebras $U_q(D_n^{(1)})$, Commun. Math. Phys. 174 (1995), 367-392. MR 96j:17022

13.
N. Jing and K. C. Misra, Vertex operators of level one $U_q(B_n^{(1)})$-modules, Lett. Math. Phys. 36 (1996), 127-143. MR 97b:17022

14.
V.G. Kac, Infinite Dimensional Lie Algebras, 3rd ed., Cambridge University Press, Cambridge, 1990. MR 92k:17038

15.
S.-J. Kang, M. Kashiwara, K.C. Misra, T. Miwa, T. Nakashima, and A. Nakayashiki , Affine crystals and vertex models , Inter. J. Mod. Phys. A 7 (1992), 449-484. MR 94a:17008

16.
A. Kato, Y. Quano and J. Shiraishi, Free boson representation of $q$-vertex operators and their correlation functions, Commun. Math. Phys. 157 (1993), 119-137. MR 95a:81125

17.
Y. Koyama, Staggered polarization of vertex models with $U_q(\widehat {sl}(n))$-symmetry, Commun. Math. Phys. 164 (1994), 277-291. MR 96h:17021

18.
A. Matsuo, A $q$-deformation of Wakimoto modules, primary fields and screening operators, Commun. Math. Phys. 151 (1993), 89-153. MR 95h:17033


Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 17B37, 17B67, 82B23, 81R10, 81R50

Retrieve articles in all Journals with MSC (1991): 17B37, 17B67, 82B23, 81R10, 81R50


Additional Information:

Naihuan Jing
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
Email: jing@eos.ncsu.edu

Kailash C. Misra
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
Email: misra@math.ncsu.edu

DOI: 10.1090/S0002-9947-99-02098-X
PII: S 0002-9947(99)02098-X
Keywords: Quantum affine algebras, $q$-vertex operators
Received by editor(s): August 30, 1996
Received by editor(s) in revised form: March 11, 1997
Additional Notes: The first author is supported in part by NSA grants MDA 904-94-H-2061 and MDA 904-96-1-0087. The second author is supported in part by NSA grant MDA 904-96-1-0013.
Copyright of article: Copyright 1999, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google