
Journal of Lie Theory 11 (2001), No. 2, 339353 Copyright Heldermann Verlag 2001 Direct Limits of Zuckerman Derived Functor Modules Amber Habib Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore Centre, 8th Mile Mysore Road, Bangalore 560059, India [Abstractpdf] We construct representations of certain direct limit Lie groups $G=\lim G^n$ via direct limits of Zuckerman derived functor modules of the groups $G^n$. We show such direct limits exist when the degree of cohomology can be held constant, and discuss some examples for the groups $Sp(p,\infty)$ and $SO(2p,\infty)$, relating to the discrete series and ladder representations. We show that our examples belong to the ``admissible'' class of Ol'shanski{\u\i}, and also discuss the globalizations of the HarishChandra modules obtained by the derived functor construction. The representations constructed here are the first ones in cohomology of nonzero degree for direct limits of noncompact Lie groups. [ Fulltextpdf (219 KB)] 