Orbital parameters for induced and restricted representations
Orbital parameters for induced and restricted representations
复制标题
诱导和限制表示的轨道参数
DOI：
10.1090/s0002-9947-1989-0930083-1
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发表时间：
1989
影响因子：
1.3
通讯作者：
R. Lipsman
中科院分区：
文献类型：
--
作者：
R. Lipsman
对于连通李群H c g，给出了诱导表示和限制表示的谱分解的一般公式。这些公式详细描述了实际谱、乘数和谱测度，这些公式是根据所谓的轨道方法中的常用参数来表示的。在幂零情况下给出了这些公式的证明。这个证明比以前用幂零代数几何得到的证明要简单得多。它也能推广到非幂零群。考虑到这一点，本文提出了许多关于半简单和对称齐次空间的新例子。同时，对指数可解齐次空间的正规子群和正规子群进行了讨论。
General formulas for the spectral decomposition of both induced and restricted representations are laid out for the case of connected Lie groups H c G. The formulas-which detail the actual spectrum, the multiplicites, and the spectral measure-are in terms of the usual parameters in the so-called orbit method. A proof of these formulas is given in the nilpotent situation. The proof is much simpler than a previously obtained proof using nilpotent algebraic geometry. It is also capable of generalization to nonnilpotent groups. With that in mind, many new examples are presented for semisimple and symmetric homogeneous spaces. Also, a start is made in the case of exponential solvable homogeneous spaces with the treatment of both normal and conormal subgroups.