The Langlands-Weissman Program for Brylinski-Deligne extensions
arXiv:1409.4039
Abstract
We describe an evolving and conjectural extension of the Langlands program for a class of nonlinear covering groups of algebraic origin studied by Brylinski-Deligne. In particular, we describe the construction of an L-group extension of such a covering group (over a split reductive group) due to Weissman, study some of its properties and discuss a variant of it. Using this L-group extension, we describe a local Langlands correspondence for covering (split) tori and unramified genuine representations, using work of Savin, McNamara, Weissman and W.W. Li. Finally, we define the notion of automorphic (partial) L-functions attached to genuine automorphic representations of the BD covering groups.
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Cited by in corpus (8)
- On Iwahori-Whittaker Functions for Metaplectic Groups
- A Generalized Theta lifting, CAP representations, and Arthur parameters
- Distinguished theta representations for certain covering groups
- Twisted doubling integrals for Brylinski-Deligne extensions of classical groups
- Hecke Modules from Metaplectic Ice
- Principal series representations of metaplectic groups
- Yang-Baxter Equations for General Metaplectic Ice
- The L-group of a covering group