On the SL(2) period integral
| dc.creator | Anandavardhanan, U. K. | |
| dc.creator | Prasad, Dipendra | |
| dc.date | 2004-12-10 | |
| dc.date | 2005-12-09 | |
| dc.date.accessioned | 2026-07-07T06:39:09Z | |
| dc.date.available | 2026-07-07T06:39:09Z | |
| dc.description | Let E/F be a quadratic extension of number fields. For a cuspidal representation $π$ of SL(2,A_E), we study the non-vanishing of the period integral on SL(2,F)\SL(2,A_F). We characterise the non-vanishing of the period integral of $π$ in terms of $π$ being generic with respect to characters of E\A_E which are trivial on A_F. We show that the period integral in general is not a product of local invariant functionals, and find a necessary and sufficient condition when it is. We exhibit cuspidal representations of SL(2,A_E) whose period integral vanishes identically while each local constituent admits an SL(2)-invariant linear functional. Finally, we construct an automorphic representation $π$ on SL(2,A_E) which is abstractly SL(2,A_F) distinguished but none of the elements in the global L-packet determined by $π$ is distinguished by SL(2,A_F). | |
| dc.identifier | https://arxiv.org/abs/math/0412213 | |
| dc.identifier | http://arxiv.org/abs/math/0412213 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100976 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 11F70; 22E55 | |
| dc.title | On the SL(2) period integral | |
| dc.type | text |