REVIEW 1 cited by
Minimal representations: spherical vectors and automorphic functionals
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
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.
Forward citations
Cited by 1 Pith paper
-
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.
Discussion (0). Continue with ORCID to comment.