Open AccessClassification of irreducible tempered representations of semisimple Lie groups
Author(s) -
Anthony W. Knapp,
Gregg J. Zuckerman
Publication year - 1976
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.73.7.2178
Subject(s) - representation theory of su , irreducible representation , (g,k) module , irreducible element , unitary state , mathematics , restricted representation , constructive , character (mathematics) , fundamental representation , algebra over a field , pure mathematics , induced representation , representation (politics) , representation of a lie group , representation theory , group (periodic table) , lie algebra , representation theory of the lorentz group , computer science , weight , chemistry , organic chemistry , geometry , process (computing) , politics , political science , law , operating system
For each connected real semisimple matrix group, one obtains a constructive list of the irreducible tempered unitary representations and their characters. These irreducible representations all turn out to be instances of a more general kind of representation, here called basic. The result completes Langland's classification of all irreducible admissible representations for such groups. Since not all basic representations are irreducible, a study is made of character identities relating different basic representations and of the commuting algebra for each basic representation.