论文标题
在整形的代数和较高尺寸的virasoro代数上对不可医院的Harish-Chandra模块进行分类
Classification of irreducible Harish-Chandra modules over full toroidal Lie algebras and higher-dimensional Virasoro algebras
论文作者
论文摘要
在本文中，我们完全将不可约合的Harish-Chandra模块分类为整个环形谎言代数，这是Aggine-Virasoro代数的天然高维模拟。作为副产品，我们还获得了在较高维的Virasoro代数上对所有可能不可约的Harish-Chandra模块的分类，该模块由Rao-Moody [Comm。数学。物理。 [1994]这些直接概括了O. Mathieu的众所周知的结果[Invent。数学。 [1992]对于古典Virasoro代数以及Billig-Futorny的最新作品[J. Reine Angew。数学。 2016年]对于更高等级的Witt代数。特别是，我们表明，在2004年Eswara Rao始终认为，尤其是在较高尺寸的Virasoro代数上的任何不可约合的Harish-Chandra模块，事实证明，要么是圆环上的张量字段模块或最高重量类型的模块，要么是自动形态扭曲的最高重量模块的商，正如Eswara Rao在2004年所推测的那样。
In this paper, we completely classify the irreducible Harish-Chandra modules over the full toroidal Lie algebra, which is a natural higher-dimensional analogue of the affine-Virasoro algebra. As a by-product, we also obtain the classification of all possible irreducible Harish-Chandra modules over the higher-dimensional Virasoro algebra, which was introduced by Rao--Moody [Comm. Math. Phys. 1994] These directly generalize the well-known result of O. Mathieu [Invent. Math. 1992] for the classical Virasoro algebra and also the recent work of Billig-Futorny [J. Reine Angew. Math. 2016] for the higher rank Witt algebra. In particular, we show that any irreducible Harish-Chandra module over the higher-dimensional Virasoro algebra turns out to be either a quotient of a module of tensor fields on a torus or a highest weight type module up to a twist of an automorphism, as conjectured by Eswara Rao in 2004.
