扭仿射 Nappi-Witten 李代数及无穷维李代数 W˜(α,β) 的表示

扭仿射Nappi-Witten李代数与无穷维李代数W˜(α,β)有很深刻的物理背景，并且它们与李理论的很多重要的研究领域密切相关，比如Kac-Moody李代数，Virasoro代数，顶点算子代数等等。我们拟对扭仿射Nappi-Witten李代数及无穷维李代数W˜(α,β)的表示展开研究。首先， 研究扭仿射Nappi-Witten李代数的Verma模，构造其顶点算子表示，分类其非零水平的不可约quasifinite-模；最后研究无穷维李代数W˜(α,β)的不可约Harish-Chandra模，中间序列模，至少具有一个非平凡有限维权空间的不可约权模的分类，另外研究其子代数的Verma模。

The twisted affine Nappi-Witten Lie algebra and infinite dimensional Lie algebra W˜(α,β) are in the profound physical backgrounds, which have close connections with many important areas of Lie theory, for instance, Kac-Moody Lie algebra, Virasoro algebra, Vertex operator algebra and so on. In this program, we plan to study the representations of the twisted affine Nappi-Witten Lie algebra and infinite dimensional Lie algebra W˜(α,β). Firstly, we shall study the Verma module, construct vertex operator representations, classify the irreducible non-zero level quasifinite module of the twisted affine Nappi-Witten Lie algebra. Finally, we shall classify the irreducible Harish-Chandra modules, modules of intermediate series, irreducible weight modules with at least one non-trivial finite dimensional weight space of W˜(α,β) and we shall study the Verma module on the subalgebra of the W˜(α,β).