On the classification of unitary highest weight modules
Abstract
In the 1980s, Enright, Howe and Wallach [ EHW ] and independently Jakobsen [ J3 ] gave a complete classification of the unitary highest weight modules. In the survey part of this paper we describe their results, and also several other related papers. In the research part of the article, we give a more direct and elementary proof of the same result for the (universal covers of the) Lie groups Sp (2 n ,ℝ), SO *(2 n ) and SU ( p , q ). (The rest of the cases are treated in our paper [ PPSST ].) We also show how to describe the set of unitary highest weight modules with a given infinitesimal character.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Japanese journal of mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 21
- Issue
- 2
- Pages
- 255–334
- Publication date
- 12 July 2026
- Language
- EN