Erratum to the Paper: A Geometric Construction of the Discrete Series for Semisimple Lie Groups

Abstract

In the above paper [2] a key role is played by a result of Borel [3], concerning discrete subgroups Г of semisimple Lie groups G. They prove that if G is linear, one can find a torsion-free Г with Г\G compact. Unfortunately we applied this result in [2] even for non-linear G, in which case the existence of such Г is seriously in doubt, as pointed out to us by P. Deligne and J. P. Serre. The difficulty is that a torsion-free subgroup of the adjoint group lifts to a cocompact subgroup Г ⊂ G which contains the (finite) center Z of G, and there may be an obstruction to removing this torsion subgroup. As it stands, [2] is correct only for linear G, and we shall now indicate how to extend the proof to cover all G.

The online version of the original chapter can be found at http://dx.doi.org/10.1007/978-94-009-8961-0_8