Duke Mathematical Journal

A twisted invariant Paley-Wiener theorem for real reductive groups

Patrick Delorme and Paul Mezo

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Let G+ be the group of real points of a possibly disconnected linear reductive algebraic group defined over R which is generated by the real points of a connected component G'. Let K be a maximal compact subgroup of the group of real points of the identity component of this algebraic group. We characterize the space of maps πtr(π(f)), where π is an irreducible tempered representation of G+ and f varies over the space of smooth, compactly supported functions on G' which are left and right K-finite. This work is motivated by applications to the twisted Arthur-Selberg trace formula

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Duke Math. J., Volume 144, Number 2 (2008), 341-380.

First available in Project Euclid: 14 August 2008

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Zentralblatt MATH identifier

Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 22E47: Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]


Delorme, Patrick; Mezo, Paul. A twisted invariant Paley-Wiener theorem for real reductive groups. Duke Math. J. 144 (2008), no. 2, 341--380. doi:10.1215/00127094-2008-039. https://projecteuclid.org/euclid.dmj/1218716302

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