Compositio Mathematica

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

Paul Mezo a1
a1 Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, Canada

Article author query
mezo p   [Google Scholar] 


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 $f \in C_{c}^{\infty}(G)$.

(Received November 6 2001)
(Accepted January 6 2003)

Key Words: Paley–Wiener theorem; twisted; disconnected real groups.

Maths Classification

22E30; 22E46.