Minimal K-types and classification of irreducible representations of reductive Lie groups
type: Item
instance of: scholarly article
title: Minimal K-types and classification of irreducible representations of reductive Lie groups
zbMATH Open document ID: 0581.22016
DOI: 10.1007/BF01083697
author: D. P. Zhelobenko
publication date: 1984-01-01T00:00:00Z
review text: Let G be a reductive Lie group and let K be its maximal compact subgroup. A new, simpler approach, based on the theory of S-algebras [see the author, Dokl. Akad. Nauk SSSR 273, 785-788 (1983; Zbl 0568.17005)], to the minimal K-types [see \textit{D. A. Vogan} jun., Ann. Math., II. Ser. 109, 1-60 (1979; Zbl 0424.22010)] is given. The proof of the main result on the single appearance of minimal K-types is very elegant and short. A classification scheme of \(\hat G\) based on K-types is sketched.
Mathematics Subject Classification ID: 22E47
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 3929328
zbMATH Keywords: irreducible representations
zbMATH Keywords: reductive Lie group
zbMATH Keywords: S-algebras
zbMATH Keywords: minimal K- types
Wikidata QID: Q115394226
reviewed by: E.T.Ljubenova-Toneva
MaRDI profile type: Publication
cites work: The algebraic structure of the representation of semisimple Lie groups. I
cites work: Q3684267
cites work: Q3684268
cites work: A proof of Blattner's conjecture
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3929328