ε factor of representations of classical groups

Abstract

We let G be the isometry group of a nondegenerate symmetric or skew-symmetric form h on a space V over some local or global field K [i.e., G = U(V, h)]. We let (L)G be the L group of G(o) = the identity component of G and r be the natural representation of this group. We develop here a theory of L functions and epsilon factors attached to this r. In particular we develop a theory of local and global zeta integrals for such G. We use very special intertwining operators; therein we require an analysis of the proper normalization of such operators. With such techniques we determine the correct epsilon factors associated to local representations. The issue of the correct local L factor is discussed.