SU\G(𝔸)/K·U

Finite- and infinite-dimensional representation of linear semisimple groups

James Lepowsky, Nolan R. Wallach

Type: Article

Publication Date: 1973-01-01

Citations: 27

DOI: https://doi.org/10.1090/s0002-9947-1973-0327978-7

Abstract

Every representation in the nonunitary principal series of a noncompact connected real semisimple linear Lie group <italic>G</italic> with maximal compact subgroup <italic>K</italic> is shown to have a <italic>K</italic>-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 <italic>G</italic>-modules, concerning which some new results are derived. Further related results on infinite-dimensional representations are also obtained.

Locations

  • Transactions of the American Mathematical Society - View - PDF

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