Finite- and infinite-dimensional representation of linear semisimple groups

Lepowsky, James; Wallach, Nolan R.

doi:10.1090/S0002-9947-1973-0327978-7

Finite- and infinite-dimensional representation of linear semisimple groups
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by James Lepowsky and Nolan R. Wallach

Trans. Amer. Math. Soc. 184 (1973), 223-246

DOI: https://doi.org/10.1090/S0002-9947-1973-0327978-7

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Abstract:

Every representation in the nonunitary principal series of a noncompact connected real semisimple linear Lie group G with maximal compact subgroup K is shown to have a K-finite cyclic vector. This is used to give a new proof of Harish-Chandra’s theorem that every member of the nonunitary principal series has a (finite) composition series. The methods of proof are based on finite-dimensional G-modules, concerning which some new results are derived. Further related results on infinite-dimensional representations are also obtained.

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Séminaire

Sophus Lie

de L’École Normale Supérieure

Théorie des algébres de Lie. Topologie des groups de Lie

17

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