On the existence of infinite-dimensional generalized Harish-Chandra modules

@article{Penkov2018OnTE,
  title={On the existence of infinite-dimensional generalized Harish-Chandra modules},
  author={Ivan Penkov and Gregg J. Zuckerman},
  journal={S{\~a}o Paulo Journal of Mathematical Sciences},
  year={2018},
  volume={12},
  pages={290-294}
}
We prove a general existence result for infinite-dimensional admissible $$(\mathfrak {g},\mathfrak {k})$$(g,k)-modules, where $$\mathfrak {g}$$g is a reductive finite-dimensional complex Lie algebra and $$\mathfrak {k}$$k is a reductive in $$\mathfrak {g}$$g algebraic subalgebra. 
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AbstractLet $$\mathfrak{g}$$ be a reductive Lie algebra over C. We say that a $$\mathfrak{g}$$ -module M is a generalized Harish-Chandra module if, for some subalgebra $$\mathfrak{k}$$ ⊂…
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Let g be a complex finite-dimensional semisimple Lie algebra and k be any sl(2)subalgebra of g. In this paper we prove an earlier conjecture by Penkov and Zuckerman claiming that the first derived…
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We make a first step towards a classification of simple generalized Harish-Chandra modules which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary algebraic reductive…
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