L-groups and parameters for covering groups

Abstract

We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. We work with all covers that arise from extensions of quasisplit reductive groups by ${\mathbf{K}}_2$ -- the class studied by Brylinski and Deligne. We use this L-group to parameterize genuine irreducible representations in many contexts, including covers of split tori, unramified representations, and discrete series for double covers of semisimple groups over $\mathbb{R}$. An appendix surveys torsors and gerbes on the étale site, as they are used in the construction of the L-group.

141 pages, This article supersedes arXiv:1501.06169, this version fixes a sign (on p.26) which is important for applications