In mathematics, endoscopic groups of a reductive algebraic groups were introduced by (Robert Langlands 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.

[edit] References

• Langlands, Robert P. (1983), Les débuts d'une formule des traces stable, Publications Mathématiques de l'Université Paris VII [Mathematical Publications of the University of Paris VII], 13, Paris: Université de Paris VII U.E.R. de Mathématiques, MR697567, http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/endoscopy.html#debuts 
• Langlands, Robert P.; Shelstad, D. (1987), "On the definition of transfer factors", Mathematische Annalen 278 (1): 219–271, doi:10.1007/BF01458070, MR909227, ISSN 0025-5831 
• Shelstad, Diana (1983), "Orbital integrals, endoscopic groups and L-indistinguishability for real groups", Conference on automorphic theory (Dijon, 1981), Publ. Math. Univ. Paris VII, 15, Paris: Univ. Paris VII, pp. 135–219, MR723184