Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjecture

DOI10.1090/tran/8258zbMath1469.11143arXiv1507.07156OpenAlexW3047180621WikidataQ113822473 ScholiaQ113822473MaRDI QIDQ5853483

Yeansu Kim

Publication date: 10 March 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.07156

zbMATH Keywords

\(L\)-packetsLanglands-Shahidi methodgeneric Arthur packet conjecture\(\mathrm{GSpin}\) groups

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items

Discrete series of odd general spin groups, Endoscopic transfer and automorphic L-functions: The case of the general spin group and the twisted symmetric and exterior square L-functions, On the generic local Langlands correspondence for 𝐺𝑆𝑝𝑖𝑛 groups, The generic dual of \(p\)-adic split \(\mathrm{SO}_{2n}\) and local Langlands parameters, Strongly positive representations of \(\mathrm{GSpin}_{2n+1}\) and the Jacquet module method (with an appendix ``Strongly positive representations in an exceptional rank-one reducibility case by Ivan Matić)

Cites Work

• The generic dual of \(p\)-adic split \(\mathrm{SO}_{2n}\) and local Langlands parameters
• Arthur packets and the Ramanujan conjecture
• Strongly positive representations of metaplectic groups
• On twisted exterior and symmetric square \(\gamma\)-factors
• Strongly positive representations of even GSpin groups
• On the standard modules conjecture
• On the Ramanujan conjecture and finiteness of poles for certain \(L\)-functions
• Local coefficients as Artin factors for real groups
• Special representations of reductive p-adic groups are not integrable
• The Langlands quotient theorem for p-adic groups
• Characterization of the local Langlands conjecture by \(\varepsilon\)-factors for pairs
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• Functoriality for the classical groups
• A simple proof of Langlands conjectures for \(\text{GL}_n\) on a \(p\)-adic field
• Local Langlands correspondence for \(\mathrm{GL}_n\) and the exterior and symmetric square \(\varepsilon\)-factors
• Generic transfer for general spin groups
• Strongly positive representations of \(\mathrm{GSpin}_{2n+1}\) and the Jacquet module method (with an appendix ``Strongly positive representations in an exceptional rank-one reducibility case by Ivan Matić)
• The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151)
• On the tempered $L$-functions conjecture
• On the generic local Langlands correspondence for 𝐺𝑆𝑝𝑖𝑛 groups
• Rankin-Selberg Convolutions
• Local L-Functions for Split Spinor Groups
• Genericity of Representations of p-Adic Sp_2n and Local Langlands Parameters
• Unipotent orbits and local L-functions
• Orbites unipotentes et pôles d'ordre maximal de la fonction μ de Harish-Chandra
• Square Integrable Representations and the Standard Module Conjecture for General Spin Groups
• Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
• On Certain L-Functions
• Induced representations of reductive ${\germ p}$-adic groups. I
• Construction of discrete series for classical 𝑝-adic groups
• DCOMPOSITION SPECTRALE ET REPRSENTATIONS SPCIALES DUN GROUPE RDUCTIF $p$-ADIQUE
• Paquets stables des s\'eries discr\`etes accessibles par endoscopie tordue; leur param\`etre de Langlands
• Correspondance de Langlands et Fonctions L des carres Exterieur et Symetrique
• Endoscopic Classification of representations of Quasi-Split Unitary Groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item