Socle filtrations of the standard Whittaker (g,K)-modules of Spin(r,1)

Abstract

Studied are the composition series of the standard Whittaker $(\mathfrak{g},K)$-modules. For a generic infinitesimal character, the structures of these modules are completely understood, but if the infinitesimal character is integral, then there are not so many cases in which the structures of them are known. In this paper, as an example of the integral case, we determine the socle filtrations of the standard Whittaker $(\mathfrak{g},K)$-modules when $G$ is the group $Spin(r,1)$ and the infinitesimal character is regular integral.