Wakimoto modules for twisted multi-loop algebra of type A1 × A1

Dexin LAN, Xiaoli KONG, Jinglian JIANG

PDF(139 KB)
PDF(139 KB)
Front. Math. China ›› 2016, Vol. 11 ›› Issue (2) : 323-338. DOI: 10.1007/s11464-015-0493-8
RESEARCH ARTICLE
RESEARCH ARTICLE

Wakimoto modules for twisted multi-loop algebra of type A1 × A1

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Abstract

We construct a class of modules for the twisted multi-loop algebra of type A1×A1 by applying Wakimoto free bosonic realization. We also discuss the structures and the irreducibility of the Fock space.

Keywords

Twisted multi-loop algebra / Wakimoto module / Free bosonic field

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Dexin LAN, Xiaoli KONG, Jinglian JIANG. Wakimoto modules for twisted multi-loop algebra of type A1 × A1. Front. Math. China, 2016, 11(2): 323‒338 https://doi.org/10.1007/s11464-015-0493-8

References

[1]
Azam S. Derivations of multi-loop algebras. Forum Math, 2007, 19: 1029–1045
CrossRef Google scholar
[2]
Batra P. Representations of twisted multi-loop Lie algebras. J Algebra, 2004, 272: 404–416
CrossRef Google scholar
[3]
Chen C, Lian H, Tan S. Automorphism group and representation of a twisted multiloop algebra. Acta Math Sin (Engl Ser), 2010, 26(1): 143–154
CrossRef Google scholar
[4]
Gao Y, Zeng Z. Hermitian representations of the extended affine Lie algebra gI2(ℂq) ˜. Adv Math, 2006, 207: 244–265
CrossRef Google scholar
[5]
Kong X. Derivations and the universal central extension of the gradation shifting toroidal Lie algebra ℒ4. J Xiamen Univ Natur Sci, 2009, 48: 305–309 (in Chinese)
[6]
Lian H, Tan S. Structure and representation for a class of infinite-dimensional Lie algebras. J Algebra, 2007, 307: 804–828
CrossRef Google scholar
[7]
Mao X, Tan S. Vertex operator representations for TKK algebras. J Algebra, 2007, 308: 704–733
CrossRef Google scholar
[8]
Mao X, Tan S. Wakimoto representation for Tits-Kantor-Koecher Lie algebras. Chinese Ann Math Ser A, 2007, 28: 329–338 (in Chinese)
[9]
Rao S E. Classification of irreducible integrable modules for multi-loop algebras with finite-dimensional weight spaces. J Algebra, 2001, 246: 215–225
CrossRef Google scholar
[10]
Tan S. TKK algebras and vertex operator representations. J Algebra, 1999, 211: 298–342
CrossRef Google scholar

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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