Abstract
The theory of endoscopic lifting created by Langlands and Shelstad concerns correspondences from stable characters of various smaller reductive groups into the (unstable virtual) characters of real forms of G. We begin with a fairly general setting for Langlands functoriality. Suppose (GΓ, W) and (H r , W H ) are extended groups (Definition 1.12). (Recall that this essentially means that G and H are complex connected reductive algebraic groups endowed with inner classes of real forms.) Suppose (v GΓ, D) and (H Γ \D H ) are E-groups for these extended groups (Definition 4.6), say with second invariants z ∈ Z(v G)θz and z H ∈ Z (v H) θz respectively. Suppose we are given an L-homomorphism
(Definition 5.1). As in Definition 10.10, fix a quotient Qof π1(vG) alg and form the corresponding quotient
of v G alg . As in (5.13)(b), we can pull this extension back by ∈ to
Define Q H to be the intersection of Q with the identity component (vHQ)0. so that
is a connected pro-finite covering of v H.
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© 1992 Springer Science+Business Media New York
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Adams, J., Barbasch, D., Vogan, D.A. (1992). Endoscopic lifting. In: The Langlands Classification and Irreducible Characters for Real Reductive Groups. Progress in Mathematics, vol 104. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0383-4_26
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DOI: https://doi.org/10.1007/978-1-4612-0383-4_26
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6736-2
Online ISBN: 978-1-4612-0383-4
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