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

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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.
Classification : 22E65
Mots-clés : direct limit group, irreducible unitary representations, derived functor modules, ladder representations 
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/JOLT_2001_11_2_a3/
@article{JOLT_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},
     zbl = {0981.22005},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2001_11_2_a3/}
}
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