Open Access
July 2019 Spectral theory for non-unitary twists
Anton Deitmar
Hiroshima Math. J. 49(2): 235-249 (July 2019). DOI: 10.32917/hmj/1564106546


Let $G$ be a Lie-group and $\mathit{\Gamma} \subset G$ a cocompact lattice. For a finite-dimensional, not necessarily unitary representation $\omega$ of $\mathit{\Gamma}$ we show that the $G$-representation on $L^2(\mathit{\Gamma} \backslash G, \omega)$ admits a complete filtration with irreducible quotients. As a consequence, we show the trace formula for non-unitary twists and arbitrary locally compact groups.


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Anton Deitmar. "Spectral theory for non-unitary twists." Hiroshima Math. J. 49 (2) 235 - 249, July 2019.


Received: 25 May 2017; Revised: 9 May 2019; Published: July 2019
First available in Project Euclid: 26 July 2019

zbMATH: 07120741
MathSciNet: MR3984993
Digital Object Identifier: 10.32917/hmj/1564106546

Primary: 11F72 , 58C40
Secondary: 22E45 , 43A99

Keywords: spectral analysis , trace formula

Rights: Copyright © 2019 Hiroshima University, Mathematics Program

Vol.49 • No. 2 • July 2019
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