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This topic has appeared in the English Wikipedia rankings 1 time. It first appeared on 2026-07-26 and was most recently seen on 2026-07-26.
In mathematics, the Langlands group is a conjectural group attached to each local or global field that satisfies properties similar to those of the Weil group. It was named after Robert Langlands by Robert Kottwitz. In Kottwitz's formulation, the Langlands group should be an extension of the Weil group by a compact group. When is local archimedean, is the Weil group of , when is local non-archimedean, is the product of the Weil group of with SU(2). When is global, the existence of is still conjectural, though James Arthur gives a conjectural description of it. The Langlands correspondence for is a "natural" correspondence between the irreducible -dimensional complex representations of and, in the global case, the cuspidal automorphic representations of , where denotes the adeles of .
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