Open AccessSingular Integrals and the Principal Series, IV
Author(s) -
Anthony W. Knapp,
Elias M. Stein
Publication year - 1975
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.72.6.2459
Subject(s) - unitary state , series (stratigraphy) , normalization (sociology) , mathematics , pure mathematics , dimension (graph theory) , algebra over a field , principal (computer security) , computer science , sociology , paleontology , biology , political science , anthropology , law , operating system
The intertwining operators that have been constructed for all the series of unitary representations appearing in the Plancherel formula of a connected real semisimple Lie group of matrices are given a new normalization and then applied in two ways. The first is to obtain dimension formulas for the commuting algebras of the unitary representations in question. The second is to establish the existence of complementary series. These bear the same relationship to the unitary representations under study that the complementary series found earlier bear to the principal series.