Mathematics – Representation Theory
Scientific paper
2002-09-24
Mathematics
Representation Theory
AMSLatex, 53 pages
Scientific paper
In the first part of this paper we study minimal representations of simply connected simple split groups of type $D_k$ or $E_k$ over local non-archimedian fields. Our main result is an explicit formula for the spherical vectors in these representations. In the case of real and complex groups such a formula was obtained recently in hep-th/0107222. We also use our techniques to study the structure of the space of smooth vectors in the minimal representation recovering some results of Magaard and Savin. In the second part we consider groups as above defined over a global field. In this situation we describe the form of the automorphic functional on the minimal representation of the corresponding adelic group.
Kazhdan David
Polishchuk Alexander
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