D4 Modular Forms
| dc.creator | Weissman, Martin H. | |
| dc.date | 2004-08-02 | |
| dc.date.accessioned | 2026-07-07T05:10:57Z | |
| dc.date.available | 2026-07-07T05:10:57Z | |
| dc.description | In this paper, we study modular forms on two simply connected groups of type $D_4$ over ${\mathbb Q}$. One group, $G_s$ is a globally split group of type $D_4$, viewed as the group of isotopies of the split rational octonions. The other, $G_c$, is the isotopy group of the rational (non-split) octonions. We study automorphic forms on $G_s$, in analogy to the work of Gross, Gan, and Savin on $G_2$; namely we study automorphic forms whose component at infinity corresponds to a quaternionic discrete series representation. We study automorphic forms on $G_c$ using Gross's formalism of ``algebraic modular forms''. Finally, we follow work of Gan, Savin, Gross, Rallis, and others, to study an exceptional theta correspondence connecting modular forms on $G_c$ and $G_s$. This can be thought of as an octonionic generalization of the Jacquet-Langlands correspondence. | |
| dc.description | 39 Pages | |
| dc.identifier | https://arxiv.org/abs/math/0408029 | |
| dc.identifier | http://arxiv.org/abs/math/0408029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72088 | |
| dc.subject | Representation Theory | |
| dc.subject | Number Theory | |
| dc.subject | 11F70; 11F30; 11F85; 11F55 | |
| dc.title | D4 Modular Forms | |
| dc.type | text |