Generalizations of the Springer correspondence and cuspidal Langlands parameters
نویسندگان
چکیده
منابع مشابه
Howe Correspondence and Springer Correspondence
Consider real reductive group G, as defined in [Wal88]. Let Π be an irreducible admissible representation of G with the distribution character ΘΠ, [Har51]. Denote by uΠ the lowest term in the asymptotic expansion of ΘΠ, [BV80]. This is a finite linear combination of Fourier transforms of nilpotent coadjoint orbits, uΠ = ∑ O cOμ̂O. As shown by Rossmann, [Ros95], the closure of the union of the ni...
متن کاملWEIGHTS IN GENERALIZATIONS OF SERRE’S CONJECTURE AND THE MOD p LOCAL LANGLANDS CORRESPONDENCE
In this mostly expository article we give a survey of some of the generalizations of Serre’s conjecture and results towards them that have been obtained in recent years. We also discuss recent progress towards a mod p local Langlands correspondence for p-adic fields and its connections with Serre’s conjecture. A theorem describing the structure of some mod p Hecke algebras for GLn is proved.
متن کاملOn the Local Langlands Correspondence
The local Langlands correspondence for GL(n) of a non-Archimedean local field F parametrizes irreducible admissible representations of GL(n, F ) in terms of representations of the Weil-Deligne group WDF of F . The correspondence, whose existence for p-adic fields was proved in joint work of the author with R. Taylor, and then more simply by G. Henniart, is characterized by its preservation of s...
متن کاملGrothendieck’s simultaneous resolution and the Springer correspondence
1.1 Symplectic structure on the cotangent bundle Let G be a semisimple algebraic group with Lie algebra g. Fix a Borel subgroup B of G, and let B = G/B be the corresponding flag variety. The cotangent bundle T ∗B comes equipped with symplectic form ω = dλ defined as follows. For x ∈ B and α ∈ T ∗ xB, let π : T ∗B → B be the projection and π∗ : TαT ∗B → TxB be its differential. Then, for ξ ∈ TαT...
متن کاملAn introduction to the local Langlands correspondence
In these notes, based on my lectures at the FRG workshop on “Characters, Liftings, and Types” at American University in June 2012, I give an introduction to the conjectural Local Langlands Correspondence (LLC), for split semisimple groups over a nonarchimedean local field. This conjecture has been evolving over the past 45 years (with roots going back much further) to the point that today’s sta...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2018
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-018-1001-8