Modules for double affine Lie algebras

doi:10.1007/s11464-015-0447-1

Front. Math. China

2016, Vol. 11

Issue (1) : 89-108 https://doi.org/10.1007/s11464-015-0447-1

RESEARCH ARTICLE

Modules for double affine Lie algebras

Naihuan JING^1,²,Chunhua WANG^1,^*(

)

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

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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.

Keywords Double affine Lie algebra Verma module irreducibility Weylmodule

Corresponding Author(s): Chunhua WANG

Issue Date: 02 December 2015

Cite this article:

Naihuan JING,Chunhua WANG. Modules for double affine Lie algebras[J]. Front. Math. China, 2016, 11(1): 89-108.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0447-1
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I1/89

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