In mathematics, endoscopic groups of reductive algebraic groups were introduced by Robert Langlands (1979, 1983) 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
- Arthur, James G. (2012). The Endoscopic Classification of Representations: Orthogonal and Symplectic Groups (PDF).
- Arthur, James G. (2012). Endoscopy bending sections.
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