The Local Langlands Conjecture for GSp(4)

By W. Gan, Shuichiro Takeda. 2007

233 citations recorded by the source corpus.

We show that the local Langlands conjecture for $Sp(2n)$ follows from that for $GSp(2n)$. In particular, we prove the local Langlands conjecture for $Sp(4)$, based on our previous work on the local Langlands conjecture for $GSp(4)$. We also determine the possible sizes of $L$-packets for $Sp(4)$.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/067384a9c5777d580b33004190e22a40475377f6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. T. Gee
2. E. Viehmann
3. Ralf Schmidt
4. Atsushi Ichino
5. David Geraghty
6. Michael Rapoport
7. W. Gan
8. Xuhua He

In Geometry and Topology

1. W. Gan
2. Michael Rapoport
3. David Geraghty
4. T. Gee
5. E. Viehmann
6. Ralf Schmidt
7. Atsushi Ichino
8. Xuhua He

In Mathematical Physics

1. W. Gan
2. Michael Rapoport
3. E. Viehmann
4. David Geraghty
5. T. Gee
6. Ralf Schmidt
7. Atsushi Ichino
8. Xuhua He

Citations in the corpus

• Towards a theory of local Shimura varieties (2014, background): “Gan (e-mail to the authors), both directions follow easily from the construction in [20].”
• Formal degrees and local theta correspondence (2013, background): “A result of [14] says that the representations π̃ and π̃∗ form an endoscopic L-packet of GSp4, but the equality deg π̃ = deg π̃∗”
• The Howe Duality Conjecture (2014, methodology): “As an example, it is the main tool used in the paper [4] to establish the local Langlands conjecture for GSp(4) and in [3] to establish the remaining cases of the so-called local Gross–Prasad conjecture.”
• Packet structure and paramodular forms (2017, methodology): “Since the results of [4] imply that the L-packets of [9] coincide with the L-packets of [2] for SO(5), we have L(s, π) = L(s, μ), the standard L-factor for the representation μ of GL(4,Qp).”
• COMPANION FORMS FOR UNITARY AND SYMPLECTIC GROUPS (2010, background): “(3) For each place v of M there is an equality of Weil-Deligne representations rec(πv) = rec(Πv), where we also denote the local Langlands correspondence of [GT07] by rec, and consider GSp4 as a subgroup of GL4.”