The local Langlands correspondence for inner forms of \(\mathrm{SL}_{n}\)

DOI10.1186/s40687-016-0079-4zbMath1394.22015arXiv1305.2638OpenAlexW1659074990WikidataQ59469006 ScholiaQ59469006MaRDI QIDQ2374087

Maarten Solleveld, Roger Plymen, Anne-Marie Aubert, Paul F. Baum

Publication date: 14 December 2016

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.2638

zbMATH Keywords

representation theorydivision algebralocal Langlands conjectureclose fields

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Representations of Lie and linear algebraic groups over local fields (22E50)

Related Items (18)

Depth and the Local Langlands Correspondence ⋮ On multiplicity in restriction of tempered representations of \(p\)-adic groups ⋮ Smooth duals of inner forms of \(\mathrm{GL}_n\) and \(\mathrm{SL}_n\) ⋮ Langlands program and Ramanujan Conjecture: A survey ⋮ Generalizations of the Springer correspondence and cuspidal Langlands parameters ⋮ The local Langlands conjecture for \(p\)-adic \(\mathrm{GSpin}_{4}\), \(\mathrm{GSpin}_{6}\), and their inner forms ⋮ On L-packets and depth for SL2(K) and its inner form ⋮ Depth-preserving property of the local Langlands correspondence for quasi-split classical groups in large residual characteristic ⋮ On input and Langlands parameters for epipelagic representations ⋮ ON THE LOCAL LANGLANDS CORRESPONDENCE FOR SPLIT CLASSICAL GROUPS OVER LOCAL FUNCTION FIELDS ⋮ Some aspects of the geometric structure of the smooth dual of $p$-adic reductive groups ⋮ Geometric structure in smooth dual and local Langlands conjecture ⋮ Conjectures about 𝑝-adic groups and their noncommutative geometry ⋮ Around the Langlands program ⋮ On twisted exterior and symmetric square \(\gamma\)-factors ⋮ Langlands parameters, functoriality and Hecke algebras ⋮ Congruences of parahoric group schemes ⋮ A Hecke algebra isomorphism over close local fields

Cites Work

• Rigid inner forms of real and \(p\)-adic groups
• Geometric structure in smooth dual and local Langlands conjecture
• Representations of \(GL(n)\) and division algebras over a p-adic field
• Arithmetic invariants of discrete Langlands parameters
• A note on \(L\)-packets
• Stable trace formula: Cuspidal tempered terms
• Representations of groups over close local fields
• L-indistinguishability and R groups for the special linear group
• Exercices dyadiques
• \({\mathcal D}\)-elliptic sheaves and the Langlands correspondence
• Characterization of the local Langlands conjecture by \(\varepsilon\)-factors for pairs
• An irreducibility result in non-zero characteristic
• Jacquet functors and unrefined minimal \(K\)-types
• The local Langlands correspondence for \(\mathrm{GL}_n\) over \(p\)-adic fields
• On the transfer of distributions: Weighted orbital integrals
• A simple proof of Langlands conjectures for \(\text{GL}_n\) on a \(p\)-adic field
• On Galois cohomology of semisimple groups over local and global fields of positive characteristic
• Galois-Kohomologie halb einfacher algebraischer Gruppen über \(p\)-adischen Körpern. I, II
• Zeta functions of simple algebras
• Notes on representation theory of non-Archimedean \(SL(n)\)
• The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151)
• On the local Langlands correspondence for non-tempered representations
• Rankin-Selberg Convolutions
• Some Examples of Square Integrable Representations of Semisimple p-Adic Groups
• Sur le dual unitaire de GL<i>_r</i>(<i>D</i>)
• On 𝐿-packets for inner forms of 𝑆𝐿_{𝑛}
• The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129)
• Non-Abelian Congruence Gauss Sums and _p -Adic Simple Algebras
• The local Langlands correspondence for GSp4 over local function fields
• Hereditary orders, Gauss sums and supercuspidal representations of GLN.
• Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
• Smooth representations of reductive p -ADIC groups: structure theory via types
• Classification of unipotent representations of simple 𝑝-adic groups, II
• Correspondance de Jacquet–Langlands pour les corps locaux de caractéristique non nulle
• A NOTE ON THE LANGLANDS CLASSIFICATION AND IRREDUCIBILITY OF INDUCED REPRESENTATIONS OF p-ADIC GROUPS
• Unitary dual ofGL(n) at archimedean places and global Jacquet–Langlands correspondence
• SL_n, Orthogonality Relations and Transfer
• The principal series of p‐adic groups with disconnected center
• Generic representations of \(\text{GL}_N\) and near local fields.
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