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 a real orthogonal group, 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 \((G, G^{\prime })\) in O(E, b), we determine explicitly the nature of its preimages \((\tilde {G}, \tilde {G^{\prime }})\) in Pin(E, b), and prove that apart from some exceptions, \((\tilde {G}, \tilde {G^{\prime }})\) is always a dual pair in Pin(E, b); then we establish the Howe correspondence for π with respect to \((\tilde {G}, \tilde {G^{\prime }})\).

在本文中，我们给出了设置（O（E，b），P i n（E，b），π）的Howe对应关系的完整图片，其中O（E，b）是实正交组P i n（E，b）是O（E，b）的两倍Pin-covering ，π是P i n（E，b）的脊椎表示。更确切地说，对于双对\（（G，G ^ {\ prime}} \）在O（E，b）中，我们明确确定其原像的性质\（（\ tilde {G}，\ tilde {G ^ {\ prime}}） \）在P i n（E，b）中，并证明除某些例外情况之外，\（（\ tilde {G}，\ tilde {G ^ {\ prime}}）\）在P i中始终是双对n（E，b）; 然后针对\（（\ tilde {G}，\ tilde {G ^ {\ prime}}）\）建立π的Howe对应关系。