1983/01/01 by Thomas J. Enright, Roger Howe, Nolan R. Wallach · 5 citations
Mathematics · Medicine · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Alzheimer's disease research and treatments
paper · doi:10.1007/978-1-4684-6730-7_7
openalex publication_date 1983/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Let G be a simply connected, connected simple Lie group with center Z. Let K be a closed maximal subgroup of G with K/Z compact and let g be the Lie algebra of G. A unitary representation (π,H) of G such that the underlying (ℊK) — module is an irreducible quotient of a Verma module for ℊℂ is called a unitary highest weight module. Harish-Chandra ([4],[5]) has shown that G admits nontrivial unitary highest weight modules precisely when (G,K) is a Hermitian symmetric pair. In this paper we give a complete classification of the unitary highest weight modules.