Direct limits of Zuckerman derived functor modules (Q2730486)

A representation of a direct limit group is called \(O\)-admissible if the group acts continuously in the strong operator topology. \(O\)-admissible representations arise as direct limits of irreducible unitary representations of the constituent groups. The main theorem in the article is about the existence of direct limits of Zuckerman's derived functor modules. Habib also generates unitary representations for the limit groups \(SO(2p,\infty)\) and \(Sp(p,\infty)\) by computing direct limits of Zuckerman modules. In the \(Sp(p,\infty)\) example he obtains ladder representations as direct limits of ladder representations of \(Sp(p,n)\).