1969/07/01 by Bertram Kostant · 297 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Finite Group Theory Research #Irreducibility #Series (stratigraphy) #Mathematics #Pure mathematics #Algebra over a field
paper · pdf · doi:10.1090/s0002-9904-1969-12235-4
published in Bulletin of the American Mathematical Society 75(4), 627-643 (American Mathematical Society)
openalex publication_date 1969/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
KOSTANT 1. Introduction. 1. By the principal series one means here the unitary representations of a semisimple Lie group G arising from induction to G by characters on MAN corresponding to characters on A. Although long conjectured to be irreducible, this family of representations has been shown to be irreducible only for special groups. For example see In the general case (all G) irreducibility has been proved by Bruhat [l] using analytic methods, only however, for the "regular" characters on A. A proof of the irreducibility of all the elements of the principal series is but one application of certain algebraic results, stated here, on modules of the universal enveloping algebra U of the Lie algebra g of G.