Minimal and next-to-minimal automorphic functions on split simply-laced groups are uniquely determined by, and explicitly reconstructible from, their Whittaker coefficients.
Minimal representations: spherical vectors and automorphic functionals
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
math.NT 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups
Minimal and next-to-minimal automorphic functions on split simply-laced groups are uniquely determined by, and explicitly reconstructible from, their Whittaker coefficients.