Langlands Classification for L-Parameters

2014/07/24 by Silberger, Allan J., Zink, Ernst-Wilhelm · 2 citations
#22G50 11F70 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1407.6494

Abstract

Let F be a non-archimedean local field and G=\bfG(F) the group of F-rational points of a connected reductive F-group. Then we have the Langlands classification of complex irreducible admissible representations π of G in terms of triples (P,σ,ν) where P⊂ G is a standard F-parabolic subgroup, σ is an irreducible tempered representation of the standard Levi-group M_P and ν∈ ℝ⊗ X^*(M_P) is regular with respect to P. Now we consider Langlands' L-parameters [ϕ] which conjecturally will serve as a system of parameters for the representations π and which are (roughly speaking) equivalence classes of representations ϕ of the absolute Galois group Γ=Gal(F|F) with image in Langlands' L-group ^LG, and we classify the possible [ϕ] in terms of triples (P,[ ^tϕ],ν) where the data (P,ν) are the same as in the Langlands classification of representations and where [ ^tϕ] is a tempered L-parameter of M_P.

Cited by

• The local Langlands conjecture
• The FPP Conjecture for p-adic Groups

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