论文标题
$ c^\ ast $ -Blocks和Crossical $ p $ ADIC Groups的交叉产品
$C^\ast$-blocks and crossed products for classical $p$-adic groups
论文作者
论文摘要
令$ g $为真实或$ p $ - 亚种还原组。我们考虑$ g $的钢化双重及其连接组件。对于真实的组，Wassermann在1987年通过非交通型几何方法证明了每个连接的组件具有一个简单的几何结构，该结构编码了诱导表示的降低性。对于$ p $ - adiC组，钢化双重的每个连接的组件都配备有有限的组动作的紧凑型圆环，我们证明Wassermann定理的版本在该动作的稳定器结构的一定几何假设下是正确的。然后，我们专注于$ g $是一个准策略符号，正交或单一组，并明确确定满足几何假设的连接组件。
Let $G$ be a real or $p$-adic reductive group. We consider the tempered dual of $G$, and its connected components. For real groups, Wassermann proved in 1987, by noncommutative-geometric methods, that each connected component has a simple geometric structure which encodes the reducibility of induced representations. For $p$-adic groups, each connected component of the tempered dual comes with a compact torus equipped with a finite group action, and we prove that a version of Wassermann's theorem holds true under a certain geometric assumption on the structure of stabilizers for that action. We then focus on the case where $G$ is a quasi-split symplectic, orthogonal or unitary group, and explicitly determine the connected components for which the geometric assumption is satisfied.
