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Theta lifts to certain cohomological representations of indefinite orthogonal groups.
- Source :
-
Research in Number Theory . 3/7/2024, Vol. 10 Issue 2, p1-27. 27p. - Publication Year :
- 2024
-
Abstract
- Howe and Tan (Bull Am Math Soc 28:1–74, 1993) investigated a degenerate principal series representation of indefinite orthogonal groups O (b + , b -) and explicitly described its composition series. In particular it contains a unique unitarizable irreducible submodule Π , which is isomorphic to a cohomological representation. In this paper we construct orthogonal automorphic forms locally corresponding to Π as theta liftings of holomorphic Mp 2 (R) cusp forms by using the Borcherds' method (Invent Math 132:491–562, 1998). We propose a special choice of Schwartz functions to define the liftings, which yields precise descriptions of their Fourier expansions. [ABSTRACT FROM AUTHOR]
- Subjects :
- *AUTOMORPHIC forms
*CUSP forms (Mathematics)
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 25220160
- Volume :
- 10
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Research in Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 175932886
- Full Text :
- https://doi.org/10.1007/s40993-024-00510-z