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endoscopic 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.
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