论文信息 - Finite- and infinite-dimensional representation of linear semisimple groups

Finite- and infinite-dimensional representation of linear semisimple groups

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 /C-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.

N. Wallach | J. Lepowsky

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