Modules of the toroidal Lie algebra $\widehat{\widehat{\mathfrak{sl}}}_{2}$

Document Type: Research Paper

Authors

1 Department of Mathematics, ‎Shanghai University, ‎Shanghai 200444‎, ‎China.

2 School of Information and Mathematics, ‎Yangtze University, ‎Jingzhou 434023‎, ‎China.

Abstract

‎Highest weight modules of the double affine Lie algebra $\widehat{\widehat{\mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

Keywords

Main Subjects

References

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History

• Receive Date: 22 May 2015
• Revise Date: 04 October 2015
• Accept Date: 04 October 2015