Certain conjectures relating unipotent orbits to automorphic representations. (English) Zbl 1128.11028
This paper is devoted to the problem of determining which Fourier coefficients an automorphic representation of a split reductive algebraic group over a global field \(F\). One can associate Fourier coefficients with unipotent orbits and these can be described combinatorially. The author discusses which unipotent orbits support, in this sense, non-zero Fourier coefficients. He combines the conclusions of a large number of previous investigations and the theory of Eisenstein series to formulate a number of conjectures on this set of unipotent orbits. The discussion treats the individual characteristics of the groups and several of the conjectures depend on the class of groups under consideration.
Reviewer: Samuel James Patterson (Göttingen)
MSC:
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 22E55 | Representations of Lie and linear algebraic groups over global fields and adèle rings |
Keywords:
automorphic representation; Fourier coefficient; split reductive group; unipotent orbit; partition; Eisenstein seriesReferences:
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