Restrictions of representations of classical groups: examples
By W. Gan, B. Gross, Dipendra Prasad. 2009
53 citations recorded by the source corpus.
In an earlier paper, we considered several restriction problems in the representation theory of classical groups over local and global fields. Assuming the Langlands-Vogan parameterization of irreducible representations, we formulated precise conjectures for the solutions of these restriction problems. In the local case, our conjectural answer is given in terms of Langlands parameters and certain natural symplectic root numbers associated to them. In the global case, the conjectural answer is expressed in terms of the central critical value or derivative of a global $L$-function. In this paper we verify several of these conjectures in certain low rank cases, using methods of base change, theta correspondence, and global arguments.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cbcf53180bf0daf7098d37db1acd197957b96511
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
- W. Gan
- Atsushi Ichino
- Wei Zhang
- Michael Rapoport
- S. Kudla
- Shuichiro Takeda
- Yannan Qiu
- Y. Sakellaridis
In Mathematical Physics
- W. Gan
- Atsushi Ichino
- Wei Zhang
- Hiraku Atobe
- Shuichiro Takeda
- Paul D. Nelson
- Michael Rapoport
- Ralf Schmidt
Citations in the corpus
- The Gross–Prasad conjecture and local theta correspondence (2014, background): “In [10], [11], [6], [7], a restriction problem in the representation theory of classical groups was studied and a precise conjecture was formulated for this restriction problem.”