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Delorme, Patrick; Mezo, Paul

A twisted invariant Paley-Wiener theorem for real reductive groups. (English) Zbl 1189.22005

Duke Math. J. 144, No. 2, 341-380 (2008).
Summary: Let \(G^+\) be the group of real points of a possibly disconnected linear reductive algebraic group defined over \(\mathbb R\) 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 \(\pi\mapsto \text{tr}(\pi(f))\), where \(\pi\) 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.

Cited in 1 Review
Cited in 8 Documents

MSC:

22E30 Analysis on real and complex Lie groups
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
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\textit{P. Delorme} and \textit{P. Mezo}, Duke Math. J. 144, No. 2, 341--380 (2008; Zbl 1189.22005)
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