Euler factors attached to unramified principal series representations (Q5903695)

Let G be a connected reductive unramified algebraic group defined over a non-archimedean local field F of characteristic zero. We use the same notation as in an earlier paper [ibid. 63, 215-217 (1987; Zbl 0628.22008)]. We fix a non-degenerate character \(\phi\) of U(F). For a regular unramified character \(\chi \in X_{reg}(T)\) of T(F), let \(\rho (D_{\chi})\) be the unique constituent of the unramified principal series representation I(\(\chi)\) which has a Whittaker model with respect to \(\phi\) (see op. cit., Theorem 2). The purpose of this note is to give a construction of an Euler factor attached to \(\rho (D_{\chi})\). A detailed account will be given elswhere.