The Local Langlands Conjecture for Sp(4)

2010/01/01 by Wee Teck Gan, Shuichiro Takeda · 2 citations
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Geometry and complex manifolds #Conjecture #Library science #Mathematics #Computer science #Combinatorics

paper · doi:10.1093/imrn/rnp203

openalex publication_date 2010/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

We show that the local Langlands conjecture for Sp2n(F) follows from that for GSp2n(F), where F is a non-Archimedean local field of characteristic 0. In particular, we prove the local Langlands conjecture for Sp4(F) based on our previous work [6] on the local Langlands conjecture for GSp4(F). We also determine the possible sizes of L-packets for Sp4(F).

Citations

• Theta correspondences for GSp(4)
• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique
• Foundations of Differentiable Manifolds and Lie Groups
• A Proof of Langlands' Conjecture on Plancherel Measures; Complementary Series of -adic groups

Cited by

• The local Langlands conjecture for GSp(4)
• Local Langlands conjectures [wikipedia]