Serie : Astérisque. Vol 398
Paru le 01/05/2018 | Broché XVI-286 pages
Professionnels
This volume proposes an extension of the Langlands program to covers of quasisplit groups, where covers are those that arise from central extensions of reductive groups by K2. By constructing an L-group for any such cover, one may conjecture a parameterization of genuine irreducible representations by Langlands parameters. Two constructions of the L-group are given, and related to each other in a final note. The proposed local Langlands conjecture for covers (LLCC) is proven for covers of split tori, spherical representations in the p-adic case, and discrete series for doublecovers of real semisimple groups. The introduction of the L-group allows one to define partial L-functions and functoriality, including base change, for representations of covering groups.