An Automorphic Theta Module for Quaternionic Exceptional Groups

Gan, Wee Teck

Canadian journal of mathematics, Tome 52 (2000) no. 4, pp. 737-756

Résumé

We construct an automorphic realization of the global minimal representation of quaternionic exceptional groups, using the theory of Eisenstein series, and use this for the study of theta correspondences.

Détail

DOI : 10.4153/CJM-2000-031-4

Mots-clés : 11F27, 11F70

Bibliographie

[GrG] [GrG] Gross, B. H. and Gan, W. T., Commutative Subrings of Certain Non-associative Rings. Math. Ann., 1999, to appear. Google Scholar

[GrS] [GrS] Gross, B. H. and Savin, G., Motives with Galois Group of Type G2: an Exceptional Theta Correspondence. Compositio Math. (2) 114(1998), 153–217. Google Scholar

[GrW] [GrW] Gross, B. H. and Wallach, N., On Quaternionic Discrete Series Representations, and Their Continuations. J. Reine Angew. Math. 481(1996), 73–123. Google Scholar

[GRS1] [GRS1] Ginzburg, D., Rallis, S. and Soudry, D., On the Automorphic Theta Representation for Simply-Laced Groups. Israel J. Math. 100(1997), 61–116. Google Scholar

[GRS2] [GRS2] Ginzburg, D., Rallis, S. and Soudry, D., A Tower of Theta Correspondences for G2. Duke Math. J. (3) 88(1997), 537–624. Google Scholar

[L] [L] Langlands, R., Euler Products. Yale Math.Monographs, 1971. Google Scholar

[Li1] [Li1] Li, J. S., Two Reductive Dual Pairs in Groups of Type E. Manuscripta Math. (2) 91(1996), 163–177. Google Scholar

[Li2] [Li2] Li, J. S., A Description of the Discrete Spectrum of SL(2), E7(25). Preprint, 1998. Google Scholar

[MS] [MS] Magaard, K. and Savin, G., Exceptional Theta Correspondences. Compositio Math. 107(1997), 89–123. Google Scholar

[MW] [MW] Moeglin, C. and Waldspurger, J-L., Spectral Decomposition and Eisenstein Series. Cambridge University Press, 1996. Google Scholar

[R] [R] Rumelhart, K., An Automorphic Theta Module for a Rank 2 Form of E6. Preprint, 1997. Google Scholar

[R2] [R2] Rumelhart, K., Minimal Representations of Exceptional p-adic Groups. Represent. Theory 1, 1997. Google Scholar

[S] [S] Savin, G., The Dual Pair PGL2 ×GJ: GJ is the Automorphism Group of the Jordan Algebra. Invent.Math. 118(1994), 141–160. Google Scholar

[SG] [SG] Savin, G. and Gan, W. T., The Dual Pair G2 × PU3(D): the p-adic case. Canad. J. Math. (1) 51(1999), 130–146. Google Scholar

[T] [T] Torasso, P., Méthode des orbites de Kirillov-Duflo et représentations minimales des groupes simples sur un corps local de caractéristique nulle. DukeMath. J. (2) 90(1997), 261–378. Google Scholar

[Wa] [Wa] Wallach, N., Real Reductive Groups II. Academic Press, 1992. Google Scholar

[Wr] [Wr] Wright, D., The Adelic Zeta Function associated to the space of Binary Cubic Forms. Math. Ann. 270(1985), 503–534. Google Scholar