Geodesic
Direct Limits of Zuckerman Derived Functor Modules
Journal of Lie theory, Tome 11 (2001) no. 2, pp. 339-353.

Voir la notice de l'article provenant de la source Heldermann Verlag

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 Harish-Chandra modules obtained by the derived functor construction. The representations constructed here are the first ones in cohomology of non-zero degree for direct limits of non-compact Lie groups. 
@article{JLT_2001_11_2_JLT_2001_11_2_a3,
     author = {A. Habib },
     title = {Direct {Limits} of {Zuckerman} {Derived} {Functor} {Modules}},
     journal = {Journal of Lie theory},
     pages = {339--353},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2001},
     url = {http://geodesic.mathdoc.fr/item/JLT_2001_11_2_JLT_2001_11_2_a3/}
}
TY  - JOUR
AU  - A. Habib 
TI  - Direct Limits of Zuckerman Derived Functor Modules
JO  - Journal of Lie theory
PY  - 2001
SP  - 339
EP  - 353
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2001_11_2_JLT_2001_11_2_a3/
ID  - JLT_2001_11_2_JLT_2001_11_2_a3
ER  - 
%0 Journal Article
%A A. Habib 
%T Direct Limits of Zuckerman Derived Functor Modules
%J Journal of Lie theory
%D 2001
%P 339-353
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2001_11_2_JLT_2001_11_2_a3/
%F JLT_2001_11_2_JLT_2001_11_2_a3
A. Habib . Direct Limits of Zuckerman Derived Functor Modules. Journal of Lie theory, Tome 11 (2001) no. 2, pp. 339-353. http://geodesic.mathdoc.fr/item/JLT_2001_11_2_JLT_2001_11_2_a3/