Abstract
We present an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and local) model, which generalizes the Whittaker model. Here we consider linear groups, but our construction also extends to arbitrary degree metaplectic coverings; this will be the topic of an upcoming work.
| Original language | English |
|---|---|
| Pages (from-to) | 985-1068 |
| Number of pages | 84 |
| Journal | Inventiones Mathematicae |
| Volume | 217 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Sep 2019 |
Bibliographical note
Publisher Copyright:© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
Funding
Part of this work was done while the fourth named author was a Zassenhaus Assistant Professor at The Ohio State University, under the supervision of Jim Cogdell. Eyal wishes to express his gratitude to Jim for his kind encouragement and support. We thank the referee for a very careful reading of the manuscript and for many helpful suggestions. Eyal dedicates his part of the work to his beloved Sophie Kaplan who passed away unexpectedly a few weeks before the submission of the first version of this work.
| Funders | Funder number |
|---|---|
| National Science Foundation | 1801497 |
| Ohio State University | |
| Horizon 2020 Framework Programme | 637912 |