Endoscopic group

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title: "Endoscopic group" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["automorphic-forms", "langlands-program"] description: "Mathematical group" topic_path: "general/automorphic-forms" source: "https://en.wikipedia.org/wiki/Endoscopic_group" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Mathematical group ::

In mathematics, endoscopic groups of reductive algebraic groups were introduced by in his work on the stable trace formula.

Roughly speaking, an endoscopic group H of G is a quasi-split group whose L-group is the connected component of the centralizer of a semisimple element of the L-group of G.

In the stable trace formula, unstable orbital integrals on a group G correspond to stable orbital integrals on its endoscopic groups H. The relation between them is given by the fundamental lemma.

References

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