An Automorphic Theta Module for Quaternionic Exceptional Groups

2000 ◽  
Vol 52 (4) ◽  
pp. 737-756 ◽  
Author(s):  
Wee Teck Gan
Keyword(s):  
Eisenstein Series ◽  
Minimal Representation ◽  
Exceptional Groups ◽  
Theta Correspondences

AbstractWe 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.

scholarly journals R4 couplings, the fundamental membrane and exceptional theta correspondences

2001 ◽  
Vol 2001 (03) ◽  
pp. 036-036 ◽  
Author(s):  
Boris Pioline ◽  
Hermann Nicolai ◽  
Jan Plefka ◽  
Andrew Waldron
Keyword(s):  
Theta Correspondences

A tower of theta correspondences for $G_2$

1997 ◽  
Vol 88 (3) ◽  
pp. 537-624 ◽  
Author(s):  
David Ginzburg ◽  
Stephen Rallis ◽  
David Soudry
Keyword(s):  
Theta Correspondences

scholarly journals The multiplicity one conjecture for local theta correspondences

2010 ◽  
Vol 184 (1) ◽  
pp. 117-124 ◽  
Author(s):  
Jian-Shu Li ◽  
Binyong Sun ◽  
Ye Tian
Keyword(s):  
Multiplicity One ◽  
Theta Correspondences

scholarly journals Compositions of theta correspondences

2005 ◽  
Vol 190 (2) ◽  
pp. 225-263 ◽  
Author(s):  
Hongyu He
Keyword(s):  
Theta Correspondences

scholarly journals Dichotomy for generic supercuspidal representations ofG2

2011 ◽  
Vol 147 (3) ◽  
pp. 735-783
Author(s):  
Gordan Savin ◽  
Martin H. Weissman
Keyword(s):  
Irreducible Representation ◽  
Irreducible Representations ◽  
Supercuspidal Representations ◽  
Theta Correspondences

AbstractThe local Langlands conjectures imply that to every generic supercuspidal irreducible representation ofG2over ap-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6or PGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations ofG2and other representations of PGSp6and PGL3. This correspondence arises from theta correspondences inE6andE7, analysis of Shalika functionals, and spin L-functions. Our main result reduces the conjectural Langlands parameterization of generic supercuspidal irreducible representations ofG2to a single conjecture about the parameterization for PGSp6.

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