A reciprocal branching problem for automorphic representations and global Vogan packets
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Dihua Jiang
Abstract
Let G be a group and let H be a subgroup of G. The classical branching rule (or symmetry breaking) asks: For an irreducible representation π of G, determine the occurrence of an irreducible representation σ of H in the restriction of π to H. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation σ of H, find an irreducible representation π of G such that σ occurs in the restriction of π to H. For automorphic representations of classical groups, the branching problem has been addressed by the well-known global Gan–Gross–Prasad conjecture. In this paper, we investigate the reciprocal branching problem for automorphic representations of special orthogonal groups using the twisted automorphic descent method as developed in [13]. The method may be applied to other classical groups as well.
Funding statement: The first named author is partially supported by NSF grant DMS-1600685 and DMS-1901802. The second named author is partially supported by NSF grants DMS-1702218, DMS-1848058, and by start-up funds from the Department of Mathematics at Purdue University. The third named author is partially supported by NSFC grant No.11501382 and by the Fundamental Research Funds for the Central Universities.
Acknowledgements
Parts of this paper were written in the Spring of 2016 when the third named author visited the School of Mathematics, University of Minnesota. He appreciates very much the hospitality and comfortable working condition provided by the School of Mathematics. We would like to thank Lei Zhang for helpful comments. Finally, we thank the referee very much for both the careful reading of our manuscript, and also the valuable comments and suggestions, which well improve the exposition of the paper.
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Articles in the same Issue
- Frontmatter
- Sharp one-sided curvature estimates for fully nonlinear curvature flows and applications to ancient solutions
- Łojasiewicz–Simon gradient inequalities for analytic and Morse–Bott functions on Banach spaces
- Geometric estimates for complex Monge–Ampère equations
- Mukai’s program (reconstructing a K3 surface from a curve) via wall-crossing
- Remarks on the self-shrinking Clifford torus
- Regularity of Lagrangian flows over RCD*(K, N) spaces
- Convergence of the Chern–Moser–Beloshapka normal forms
- A reciprocal branching problem for automorphic representations and global Vogan packets
Articles in the same Issue
- Frontmatter
- Sharp one-sided curvature estimates for fully nonlinear curvature flows and applications to ancient solutions
- Łojasiewicz–Simon gradient inequalities for analytic and Morse–Bott functions on Banach spaces
- Geometric estimates for complex Monge–Ampère equations
- Mukai’s program (reconstructing a K3 surface from a curve) via wall-crossing
- Remarks on the self-shrinking Clifford torus
- Regularity of Lagrangian flows over RCD*(K, N) spaces
- Convergence of the Chern–Moser–Beloshapka normal forms
- A reciprocal branching problem for automorphic representations and global Vogan packets
