On quaternionic discrete series representations, and their continuations.
On quaternionic discrete series representations, and their continuations.
复制标题
关于四元数离散级数表示及其延续。
DOI：
10.1515/crll.1996.481.73
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
B. Gross
中科院分区：
文献类型：
--
作者：
N. Wallach;B. Gross
在实约化群G的离散级数表示中，研究最简单的族是全纯离散级数。当对称空间G/K具有G-不变复结构时，这些表示是存在的，当限制在K的中心的一维环面S时，它们是可容许的。它们可以被构造为G/K上的某些全纯向量丛的解析截面的äS空间。在(g，K)模范畴中，全纯离散级数产生可酉化的最高权模。其它具有最高权的有趣的单元化模可以通过全纯离散级数的“解析延拓”来构造(参看。[WL]))。
Among the discrete series representations of a real reductive group G, the simplest family to study are the holomorphic discrete series. These representations exist when the Symmetrie space G/ K has a G-invariant complex structure, and are admissible when restricted to a 1-dimensional torus S in the center of K. They can be constructed äs spaces of analytic sections of certain holomorphic vector bundles on G /K. In the category of (g, K)modules, holomorphic discrete series give rise to unitarizable highest weight modules. Other interesting unitarizable modules with a highest weight can be constructed by "analytic continuation" of the holomorphic discrete series (cf. [Wl]).