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Endoscopy and the transfer from GSp(4) to GL(4)
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Bogume Jang
Published/Copyright:
February 28, 2013
Abstract
We prove Jiang's conjecture (1996) to show the existence of an L-function of a cuspidal representation of GSp(4,𝔸) × GSp(4,𝔸) which has a pole of order 2 at s = 1, even for globally generic representations. Moreover, we show that if a cuspidal representation π of GSp(4,𝔸) comes from GSO(4,𝔸), then π is the Weil transfer of Π1 ⊗ Π2 realized as a representation of GSO(4,𝔸) where the Πi are irreducible automorphic cuspidal representations of GL(2,𝔸). This agrees with the Langlands functoriality principle as GSO(4,𝔸) is an endoscopic group for GSp(4,𝔸).
This paper is a part of my thesis at Purdue with supervising of Freydoon Shahidi. I would like to thank him for many helpful discussions.
Received: 2012-1-13
Revised: 2012-10-8
Published Online: 2013-2-28
Published in Print: 2015-1-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E
- Achievable sets in ℤn
- A criterion on oscillation and variation for the commutators of singular integral operators
- Some 𝐇1𝔉-groups with unbounded torsion and a conjecture of Kropholler and Mislin
- Goodwillie calculus and Whitehead products
- Computing Borel's regulator
- Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
- BSDE and generalized Dirichlet forms: The infinite dimensional case
- Faithful representations of infinite-dimensional nilpotent Lie algebras
- Locally finitely presented categories with no flat objects
- A common generalization of metric, ultrametric and topological fixed point theorems
- Correction to A common generalization of metric, ultrametric and topological fixed point theorems [Forum Math. 27 (2015), 303–327]
- Erdős–Rényi graph, Szemerédi–Trotter type theorem, and sum-product estimates over finite rings
- Minimal support results for Schrödinger equations
- Dynamics for the focusing, energy-critical nonlinear Hartree equation
- A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory
- On effective determination of Maass forms from central values of Rankin–Selberg L-function
- On embedding left-ordered groups into division rings
- Conservation property of symmetric jump-diffusion processes
- Irreducible representations of Leavitt path algebras
- Commutators of elements of coprime orders in finite groups
- Endoscopy and the transfer from GSp(4) to GL(4)
- Cycles in Leavitt path algebras by means of idempotents
- On volumes determined by subsets of Euclidean space
