Geodesic
Direct Limits of Zuckerman Derived Functor Modules
Journal of Lie theory, Tome 11 (2001) no. 2, pp. 339-353 Cet article a éte moissonné depuis la source Heldermann Verlag

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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},
     year = {2001},
     volume = {11},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2001_11_2_JLT_2001_11_2_a3/}
}
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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/