Strictly small representations and a reduction theorem for the unitary dual
Author(s)Salamanca-Riba, Susana A.; Vogan, David
To any irreducible unitary representation X of a real reductive Lie group we associate in a canonical way, a Levi subgroup Gsu and a representation of this subgroup. Assuming a conjecture of the authors on the infinitesimal character of X, we show that X is cohomologically induced from a unitary representation of the subgroup Gsu. This subgroup is in some cases smaller than the subgroup Gu that the authors attached to X in earlier work. In those cases this provides a further reduction to the classification problem.
First published in Representation Theory in Vol 5, 2001. Published by the American Mathematical Society.
American Mathematical Society
Representation Theory 5 (2001), 93-110