ε factor of representations of classical groups - Piatetski-Shapiro, I. (1986)
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 ε 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 ε factors associated to local representations. The issue of the correct local L factor is discussed.