论文标题
Laplace操作员在均质矢量束上的共鸣在真实等级的对称空间上
Resonances of the Laplace operator on homogeneous vector bundles on symmetric spaces of real rank-one
论文作者
论文摘要
我们研究了拉普拉斯作用在非连体类型的riemannian对称空间上的均匀载体束的紧凑型截面上的共振。假定对称空间具有排名一个，但定义向量束的$ k $的不可约表示$τ$是任意的。我们确定共鸣。在$τ$发生在球形主系列中的其他假设下，我们确定共振表示。它们都是不可约的。我们发现他们的Langlands参数，它们的波前集合，并确定其中哪些是单位化的。
We study the resonances of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type. The symmetric space is assumed to have rank-one but the irreducible representation $τ$ of $K$ defining the vector bundle is arbitrary. We determine the resonances. Under the additional assumption that $τ$ occurs in the spherical principal series, we determine the resonance representations. They are all irreducible. We find their Langlands parameters, their wave front sets and determine which of them are unitarizable.
