On the unitary dual of real reductive Lie groups and the \(A_g(\lambda)\) modules: The strongly regular case
Let \(G\) be a semisimple Lie group which is connected and has finite center. Let \(\pi\) be an irreducible unitary representation whose infinitesimal character is strongly regular and real. D. Vogan and G. Zuckerman conjectured in the course of the (unsolved) classification problem of the unitary dual of \(G\) that \(\pi\) must be isomorphic to a Zuckerman module derived from a one dimensional unitary character of a Levi subgroup. This conjecture is proved in the present paper. The method goes back to ideas of D. Vogan and the author who proposed a strategy for solving the classification problem by reducing it to groups of lower dimension.
scientific article; zbMATH DE number 1425186
scientific article