On the decomposition of Langlands subrepresentations for a group in the Harish-Chandra class

Abstract

When a group G G is in the Harish-Chandra class, the goal of classifying its tempered representations and the goal of decomposing the Langlands subrepresentation for any of its standard representations are equivalent. The main result of this work is given in Theorem (5.3.5) that consists of a formula for decomposing any Langlands subrepresentation for the group G G . The classification of tempered representations is a consequence of this theorem (Corollary (5.3.6)).