Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 2: 323 - 338

DOI: https://doi.org/10.1007/s11464-015-0493-8

RESEARCH ARTICLE

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

  • Dexin LAN , 1 ,
  • Xiaoli KONG 2 ,
  • Jinglian JIANG 1
Expand
  • 1. Department of Mathematics and Computer, Wuyi University, Wuyishan 354300, China
  • 2. Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA

Received date: 21 Jan 2015

Accepted date: 01 Jul 2015

Published date: 18 Apr 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

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.

Key words： Twisted multi-loop algebra; Wakimoto module; Free bosonic field

Cite this article

Dexin LAN , Xiaoli KONG , Jinglian JIANG . Wakimoto modules for twisted multi-loop algebra of type A1 × A1[J]. Frontiers of Mathematics in China, 2016 , 11(2) : 323 -338 . DOI: 10.1007/s11464-015-0493-8

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Azam S. Derivations of multi-loop algebras. Forum Math, 2007, 19: 1029–1045

DOI

2
Batra P. Representations of twisted multi-loop Lie algebras. J Algebra, 2004, 272: 404–416

DOI

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

DOI

4
Gao Y, Zeng Z. Hermitian representations of the extended affine Lie algebra gI2(ℂq) ˜. Adv Math, 2006, 207: 244–265

DOI

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

DOI

7
Mao X, Tan S. Vertex operator representations for TKK algebras. J Algebra, 2007, 308: 704–733

DOI

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

DOI

10
Tan S. TKK algebras and vertex operator representations. J Algebra, 1999, 211: 298–342

DOI

Options
Outlines

/

〈 〉