Journal of Lie Theory

no. 2
Direct Limits of Zuckerman Derived Functor Modules
Journal of Lie Theory, Volume 11 (2001) no. 2, pp. 339-353
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.
DOI: 10.5802/jolt.236
Classification: 22E65
Keywords: direct limit group, irreducible unitary representations, derived functor modules, ladder representations 
@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},
     doi = {10.5802/jolt.236},
     zbl = {0981.22005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.236/}
}
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%J Journal of Lie Theory
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A. Habib. Direct Limits of Zuckerman Derived Functor Modules. Journal of Lie Theory, Volume 11 (2001) no. 2, pp. 339-353. doi: 10.5802/jolt.236

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