Pin-group中的对偶对和相应旋量表示的对偶
Dual pairs in the Pin-group and duality for the corresponding spinorial representation
摘要：
本文给出了集合（$O(E, b), Pin(E, b), Π$）的Howe对应的完整图象，其中$O(E, b)$是正交群（实数或复数），$Pin(E, b)$是$O(E, b)$的二重Pin覆盖，$Π$是$Pin(E, b)$的旋量表示.更准确地说，对于$O(E, b)$中的对偶对（$G, G'$），我们明确地确定了它在$Pin(E, b)$中的原像$(\tilde{G}, \tilde{G'})$的性质，并证明了除了某些例外，$(\tilde{G}, \tilde{G'})$总是$Pin(E, b)$中的对偶对;然后我们建立了$Π$关于$(\tilde{G}, \tilde{G'})$的Howe对应。
英文摘要：
In this paper, we give a complete picture of Howe correspondence for the setting ($O(E, b), Pin(E, b), Π$), where $O(E, b)$ is an orthogonal group (real or complex), $Pin(E, b)$ is the two-fold Pin-covering of $O(E, b)$, and $Π$ is the spinorial representation of $Pin(E, b)$. More precisely, for a dual pair ($G, G'$) in $O(E, b)$, we determine explicitly the nature of its preimages $(\tilde{G}, \tilde{G'})$ in $Pin(E, b)$, and prove that apart from some exceptions, $(\tilde{G}, \tilde{G'})$ is always a dual pair in $Pin(E, b)$; then we establish the Howe correspondence for $Π$ with respect to $(\tilde{G}, \tilde{G'})$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
