Certain categories of modules for twisted affine Lie algebras

doi:10.1007/s11464-012-0203-8

Front Math Chin

2012, Vol. 7

Issue (6) : 1073-1093 https://doi.org/10.1007/s11464-012-0203-8

RESEARCH ARTICLE

Certain categories of modules for twisted affine Lie algebras

Yongcun GAO(

), Jiayuan FU

School of Science, Communication University of China, Beijing 100024, China

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Abstract

In this paper, using generating functions, we study two categories ? and ? of modules for twisted affine Lie algebras g^[σ], which were firstly introduced and studied for untwisted affine Lie algebras by H. -S. Li [Math Z, 2004, 248: 635-664]. We classify integrable irreducible g^[σ]-modules in categories ? and ?, where ? is proved to contain the well-known evaluation modules and ? to unify highest weight modules, evaluation modules and their tensor product modules. We determine also the isomorphism classes of those irreducible modules.

Keywords Twisted affine Lie algebra module category

Corresponding Author(s): GAO Yongcun,Email:gaoycjy@cuc.edu.cn

Issue Date: 01 December 2012

Cite this article:

Jiayuan FU,Yongcun GAO. Certain categories of modules for twisted affine Lie algebras[J]. Front Math Chin, 2012, 7(6): 1073-1093.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0203-8
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I6/1073

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