2013/05/17 by Xiangqian Guo, Kaiming Zhao, Guo, Xiangqian +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.1305.4059
In this paper we construct a class of new irreducible modules over untwisted affine Kac-Moody algebras \widetilde\mathfrakg, generalizing and including both highest weight modules and Whittaker modules. These modules allow us to obtain a complete classification of irreducible \widetilde\mathfrakg-modules on which the action of each root vector in \widetilde\mathfrakn+ is locally finite, where \widetilde\mathfrakn+ is the locally nilpotent subalgebra (or positive part) of \widetilde\mathfrakg. The necessary and sufficient conditions for two such irreducible \widetilde\mathfrakg-modules to be isomorphic are also determined. In the second part of the paper, we use the "shifting technique" to obtain a necessary and sufficient condition for the tensor product of irreducible integrable loop \widetilde\mathfrakg-modules and irreducible integrable highest weight \widetilde\mathfrakg-modules to be simple. This tensor product problem was originally studied by Chari and Pressley 28 years ago.