论文标题
Nilmanifolds附加的交换均匀矢量束
On commutative homogeneous vector bundles attached to nilmanifolds
论文作者
论文摘要
如果我们考虑在g/k上而不是均质空间g/k和矩阵值函数而不是标量值函数，则可以将Gelfand对（G，K）的概念推广。这给出了交换均匀矢量束的定义。成为gelfand对是成为交换均匀矢量束的必要条件。对于g/k是具有正方形综合表示的尼尔曼群岛的情况，在上一篇文章中，我们确定了一个大型交换同质矢量束的大家庭。在本文中，我们完成了分类。
The notion of Gelfand pair (G, K) can be generalized if we consider homogeneous vector bundles over G/K instead of the homogeneous space G/K and matrix-valued functions instead of scalar-valued functions. This gives the definition of commutative homogeneous vector bundles. Being a Gelfand pair is a necessary condition of being a commutative homogeneous vector bundle. For the case in which G/K is a nilmanifold having square-integrable representations, in a previous article we determined a big family of commutative homogeneous vector bundles. In this paper, we complete that classification.
