Hiroshima Mathematical Journal

Spectral theory for non-unitary twists

Anton Deitmar

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Abstract

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.

Article information

Source
Hiroshima Math. J., Volume 49, Number 2 (2019), 235-249.

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

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1564106546

Digital Object Identifier
doi:10.32917/hmj/1564106546

Mathematical Reviews number (MathSciNet)
MR3984993

Zentralblatt MATH identifier
07120741

Subjects
Primary: 11F72: Spectral theory; Selberg trace formula 58C40: Spectral theory; eigenvalue problems [See also 47J10, 58E07]
Secondary: 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 43A99: None of the above, but in this section

Keywords
spectral analysis trace formula

Citation

Deitmar, Anton. Spectral theory for non-unitary twists. Hiroshima Math. J. 49 (2019), no. 2, 235--249. doi:10.32917/hmj/1564106546. https://projecteuclid.org/euclid.hmj/1564106546


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