## Hiroshima Mathematical Journal

### Spectral theory for non-unitary twists

Anton Deitmar

#### 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
Revised: 9 May 2019
First available in Project Euclid: 26 July 2019

https://projecteuclid.org/euclid.hmj/1564106546

Digital Object Identifier
doi:10.32917/hmj/1564106546

Mathematical Reviews number (MathSciNet)
MR3984993

Zentralblatt MATH identifier
07120741

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