1976/07/01 by Anthony W. Knapp, Gregg J. Zuckerman · 54 citations
Mathematics · #(g,K)-module #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Character (mathematics) #Computer science #Constructive #Fundamental representation #Group (periodic table) #Induced representation #Irreducible element #Irreducible representation #Lie algebra #Mathematics #Pure mathematics #Representation (politics) #Representation of a Lie group #Representation theory #Representation theory of SU #Representation theory of the Lorentz group #Restricted representation #Unitary state #Weight
paper · open access · doi:10.1073/pnas.73.7.2178
published in Proceedings of the National Academy of Sciences 73(7), 2178-2180 (National Academy of Sciences)
openalex publication_date 1976/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
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.