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Endoscopy for \(\text{Mp} (2n, \mathbb{R})\). (English) Zbl 0942.22010

The metaplectic group \(Mp(2n,\mathbb{R})\) plays an important role in the theory of automorphic forms, but since it is nonlinear, the \(L\)-group machinery is not available. To get analogues of stable conjugacy, \(L\)-packets of representations or endoscopy one has to translate these notions into purely group theoretical terms. By recent work of J. Adams and D. Barbasch it emerges that this is possible. Based on work of J. Adams, in the present paper there is given a theory of endoscopy for this group. It is shown that the transfer of orbital integrals holds and the functoriality of the dual lifting of characters.

MSC:

22E30 Analysis on real and complex Lie groups
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