Jacquet–Langlands–Shimizu correspondence for theta lifts to <i>GSp</i>(2) and its inner forms I: An explicit functorial correspondence
-
- Narita Hiro-aki
- Graduate School of Science and Technology, Kumamoto University
Bibliographic Information
- Other Title
-
- Jacquet-Langlands-Shimizu correspondence for theta lifts to GSp(2) and its inner forms(1)An explicit functorial correspondence
- Jacquet–Langlands–Shimizu correspondence for theta lifts to $GSp(2)$ and its inner forms I: An explicit functorial correspondence
Search this article
Abstract
<p>As was first essentially pointed out by Tomoyoshi Ibukiyama, Hecke eigenforms on the indefinite symplectic group GSp(1,1) or the definite symplectic group GSp*(2) over ℚ right invariant by a (global) maximal open compact subgroup are conjectured to have the same spinor L-functions as those of paramodular new forms of some specified level on the symplectic group GSp(2) (or GSp(4)). This can be viewed as a generalization of the Jacquet–Langlands–Shimizu correspondence to the case of GSp(2) and its inner forms GSp(1,1) and GSp*(2). </p><p>In this paper we provide evidence of the conjecture on this explicit functorial correspondence with theta lifts: a theta lift from GL(2) × B× to GSp(1,1) or GSp*(2) and a theta lift from GL(2) × GL(2) (or GO(2,2)) to GSp(2). Here B denotes a definite quaternion algebra over ℚ. Our explicit functorial correspondence given by these theta lifts are proved to be compatible with archimedean and non-archimedean local Jacquet–Langlands correspondences. Regarding the non-archimedean local theory we need some explicit functorial correspondence for spherical representations of the inner form and non-supercuspidal representations of GSp(2), which is studied in the appendix by Ralf Schmidt.</p>
Journal
-
- Journal of the Mathematical Society of Japan
-
Journal of the Mathematical Society of Japan 69 (4), 1443-1474, 2017
The Mathematical Society of Japan
- Tweet
Details 詳細情報について
-
- CRID
- 1390001205114915968
-
- NII Article ID
- 130006887117
-
- NII Book ID
- AA0070177X
-
- ISSN
- 18811167
- 18812333
- 00255645
-
- NDL BIB ID
- 028590363
-
- Text Lang
- en
-
- Data Source
-
- JaLC
- NDL
- Crossref
- CiNii Articles
-
- Abstract License Flag
- Disallowed