L-groups and parameters for covering groups

By M. Weissman. Astérisque, 2015

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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 \'etale site, as they are used in the construction of the L-group.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9809f553628d0964353a65d7ad070609143b3884