Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 1: 89 - 108

DOI: https://doi.org/10.1007/s11464-015-0447-1

RESEARCH ARTICLE

Modules for double affine Lie algebras

  • Naihuan JING 1,2 ,
  • Chunhua WANG , 1
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  • 1. School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • 2. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA

Received date: 28 Nov 2014

Accepted date: 06 Jan 2015

Published date: 02 Dec 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

Imaginary Verma modules, parabolic imaginary Verma modules,and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated,and several results are generalized from the affine Lie algebras. In particular,imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.

Key words： Double affine Lie algebra; Verma module; irreducibility; Weylmodule

Cite this article

Naihuan JING , Chunhua WANG . Modules for double affine Lie algebras[J]. Frontiers of Mathematics in China, 2016 , 11(1) : 89 -108 . DOI: 10.1007/s11464-015-0447-1

References

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1
Chang X,Tan S.A class of irreducible integrable modules for the extended baby TKK algebra. Pacific J Math, 2011, 252: 293–312

DOI

2
Chari V.Representations of affine and toroidal Lie algebras. In: Geometric Representation Theory and Extended Affine Lie Algebras. Fields Inst Commun, Vol 59. Providence: Amer Math Soc, 2011, 169–197

3
Chari V,Le T.Representations of double affine Lie algebras. In: A Tribute to C. S. Seshadri, Trends Math. Basel: Birkhäuser, 2003, 199–219

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