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Twisted trace Paley–Wiener theorems for special and general linear groups

Published online by Cambridge University Press:  04 December 2007

Paul Mezo
Paul Mezo
Affiliation:
Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, [email protected]
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Abstract

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Let G be a real special or general linear group and $\sigma_{0}$ be the transpose-inverse involution. We characterize the image of $f \mapsto {\rm tr}(\pi(f) \pi(\sigma_{0}) )$ for irreducible representations $\pi$ of $G \rtimes \langle \sigma_{0}\rangle$, and K-finite $f \in C_{c}^{\infty}(G)$.

Keywords

Paley–Wiener theoremtwisteddisconnected real groups22E3022E46
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 1 , January 2004 , pp. 205 - 227
Copyright
Foundation Compositio Mathematica 2004