The local spectrum of the Dirac operator for the universal cover of SL 2 ( R )
The local spectrum of the Dirac operator for the universal cover of SL 2 ( R )
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SL 2 ( R ) 通用覆盖的狄拉克算子的局部谱
DOI：
10.1016/j.jfa.2015.10.010
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发表时间：
2016
影响因子：
1.7
通讯作者：
Brodzki J
中科院分区：
文献类型：
--
作者：
Brodzki J
利用表示论，计算了SL 2（R）的泛覆盖群上Dirac算子的谱，证明了它是KK1（C，A）的生成元，其中A是SL 2（R）的约化C-代数.这就产生了A的K-理论的一个新的直接计算。一个基本的作用是发挥极限的离散系列表示，这是边界之间的离散和主系列的组。我们提供了一个详细的分析的狄拉克算子的局部谱和计算狄拉克上同调。
Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of SL 2 (R), exhibiting it as the generator of K K 1 (C, A), where A is the reduced C⁎-algebra of the group. This yields a new and direct computation of the K-theory of A. A fundamental role is played by the limit-of-discrete-series representation, which is the frontier between the discrete and the principal series of the group. We provide a detailed analysis of the localised spectra of the Dirac operator and compute the Dirac cohomology.