标题： 伪微分算子和康奈斯-卡斯帕夫同构 显示英文标题

标题： Pseudodifferential operators and the Connes-Kasparov isomorphism

摘要： 我们计算由在实半单李群G的对称空间上的齐次丛截面上作用的零阶、等变、适当支撑、经典伪微分算子生成的C*-范畴的K-理论。我们的结果使用了G的Connes-Kasparov同构，并且实际上等价于Connes-Kasparov同构。我们将我们的计算与David Vogan著名的将具有实无穷小特征的G的温和不可约表示参数化的方法相关联。当半单群G具有实秩一时，我们提出了并证明了对称空间上等变零阶伪微分算子的傅里叶同构定理，并用它来证明Vogan定理的K-理论版本。 显示英文摘要

摘要： We compute the K-theory of the C*-category generated by order zero, equivariant, properly supported, classical pseudodifferential operators acting on sections of homogeneous bundles over the symmetric space of a real reductive Lie group G. Our result uses the Connes-Kasparov isomorphism for G, and in fact is equivalent to the Connes-Kasparov isomorphism. We relate our computation to David Vogan's well-known parametrization of the tempered irreducible representations of G with real infinitesimal character. When the reductive group G has real rank one, we formulate and prove a Fourier isomorphism theorem for equivariant order zero pseudodifferential operators on the symmetric space, and use it to prove a K-theoretic version of Vogan's theorem.