论文标题
几乎线性纳什组表示的同源有限
Homological Finiteness of Representations of Almost Linear Nash Groups
论文作者
论文摘要
令$ g $是一个几乎是线性的NASH组，即，NASH组，纳什同构具有有限内核的纳什同构为$ \ gl_k（\ m athbb r）$。如果Schwartz同源性$ \ oh_ {i}^{\ cs}（g; v; v）$在\ bz $中的每个$ i \。我们表明，在某些温和的假设下，Schwartz部分的空间$γ^ς（x，\ se）$是perved $ g $ - vector Bundle $（x，\ se）$作为同源有限的，作为$ g $的代表。
Let $G$ be an almost linear Nash group, namely, a Nash group that admits a Nash homomorphism with finite kernel to some $\GL_k(\mathbb R)$. A smooth \Fre representation $V$ with moderate growth of $G$ is called homologically finite if the Schwartz homology $\oH_{i}^{\CS}(G;V)$ is finite dimensional for every $i\in\BZ$. We show that the space of Schwartz sections $Γ^ς(X,\SE)$ of a tempered $G$-vector bundle $(X,\SE)$ is homologically finite as a representation of $G$, under some mild assumptions.
