Spherical Representations

Abstract

This section deals with a special class of local non-archimedean representations of G ^J The so-called spherical representations are characterized by the existence of a non-zero vector fixed by the compact-open subgroup G ^J ($\mathcal{O}$), where ($\mathcal{O}$);is the ring of integers in F. For global considerations it is always necessary to have sufficient information on spherical representations.