The L-group of a covering group

Abstract

We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field $F$ by a complex reductive group. The L-group depends on an extension of a quasisplit reductive $F$-group by ${\mathbf{K}}_2$, a positive integer $n$ (the degree of the cover), an injective character $\epsilon :{\mu }_n\to {\mathbb{C}}^{\times }$, and a separable closure of $F$. Our L-group is consistent with previous work on covering groups, and its construction is contravariantly functorial for certain well-aligned homomorphisms. An appendix surveys torsors and gerbes on the étale site, as they are used in a crucial step in the construction.

arXiv comment54 pages

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• The Gindikin-Karpelevich Formula and Constant Terms of Eisenstein Series for Brylinski-Deligne Extensions
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