On descent and the generic packet conjecture

2016/05/05 by Sandeep Varma · 3 citations
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · doi:10.1515/forum-2015-0113

openalex publication_date 2016/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

Abstract Suppose F is a p -adic field, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>H</m:mi> <m:mn>1</m:mn> </m:msub> </m:math> H₁ is (a z -extension of) a group that is twisted endoscopic to a connected reductive quasi-split group G over F . Suppose G satisfies the strong form of the generic packet conjecture (also called tempered packet conjecture in literature). Under certain assumptions, we show that the twisted endoscopic character identities associated to this situation imply the strong form of the generic packet conjecture for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>H</m:mi> <m:mn>1</m:mn> </m:msub> </m:math> H₁ . This generalizes a result of T. Konno, and lets us deduce, under the assumption that appropriate character identities are satisfied, the generic packet conjecture for general spin (GSpin) groups.

Citations

• Caractères tordus des représentations admissibles

Cited by

• On sharpness in Local Converse Theorems for classical groups and G₂
• On the wavefront sets associated with theta representations
• Simple supercuspidal L-packets of quasi-split classical groups

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