Minimal Representations: Spherical Vectors and Automorphic Functionals
نویسندگان
چکیده
In the first part of this paper we study minimal representations of simply connected simple split groups G of type Dk or Ek over local nonarchimedian fields. Our main result is an explicit formula for the spherical vectors in these representations. In the case of groups over R and C, such a formula was obtained recently in [8]. We also use our techniques to study the structure of the space of smooth vectors in the minimal representation. In the second part we consider groups G as above defined over a global field K. In this situation we describe the form of the automorphic functional on the minimal representation of the corresponding adelic group.
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