Erratum to: Cohomology of Arithmetic Groups

with Infinite Dimensional Coefficient Spaces

cf. Documenta Math. 10, (2005) 199–216

Anton Deitmar and Joachim Hilgert

Received: May 8, 2006

Communicated by Patrick Delorme

Abstract. A correction of an error in the proof of Lemma 5.3 is given.

2000 Mathematics Subject Classification: 11F75

In the first paragraph of the proof of Lemma 5.3 of the above paper it is claimed that C^{∞}(G, π) is nuclear for π an irreducible admissible representation of G. This does not hold, for it implies that the subspace of constant functions, i.e., π itself, is also nuclear. Now π can be a Hilbert-representation and a Hilbert space is only nuclear if it is finite dimensional. It was the aim of that paragraph to give a proof that π^{∞} is nuclear. This can be seen as follows: First assume that π is induced from a minimal parabolic. Then π^{∞} may, in the compact model, be interpreted as the space of smooth sections of a vector bundle over the compact manifold K/M. Hence π^{∞} is nuclear. By the results of Casselman [10], every π^{∞} may be embedded topologically into an induced representation as above, therefore is nuclear.

Anton Deitmar

Mathematisches Institut Auf der Morgenstelle 10 72076 Tübingen Germany deitmar@uni-tuebingen.de Joachim Hilgert Universität Paderborn Fakultät für Elektrotechnik, Informatik und Mathematik Warburger Str. 100 33098 Paderborn, Germany hilgert@math.uni-paderborn.de

Documenta Mathematica 11 (2006) 241–241

242

Documenta Mathematica 11 (2006)