Spectral theory for non-unitary twists

Abstract

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