ON THE AUTOMORPHIC THETA-REPRESENTATION FOR SIMPLY LACED GROUPS

Authors
GINZBURG D RALLIS S SOUDRY D
Citation
D. Ginzburg et al., ON THE AUTOMORPHIC THETA-REPRESENTATION FOR SIMPLY LACED GROUPS, Israel Journal of Mathematics, 100, 1997, pp. 61-116
Citations number
22
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Israel Journal of Mathematics → ACNP
ISSN journal
00212172
Volume
100
Year of publication
1997
Pages
61 - 116
Database
ISI
SICI code
0021-2172(1997)100:<61:OTATFS>2.0.ZU;2-0
Abstract
We construct an automorphic realization of the minimal representation of a split, simply laced group G, over a number field. The realization is by a residue, at a certain point, of an Eisenstein series, induced from the Borel subgroup. This residue representation is square integr able and defines the automorphic theta representation. It has ''very f ew'' Fourier coefficients, which turn out to have some extra invarianc e properties.