Minimal K-types and classification of irreducible representations of reductive Lie groups
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.
scientific article; zbMATH DE number 3929328