Discretely decomposable restrictions of unitary representations of reductive Lie groups – examples and conjectures. (English) Zbl 0959.22009

Kobayashi, Toshiyuki (ed.) et al., Analysis on homogeneous spaces and representation theory of Lie groups. Based on activities of the RIMS Project Research ’97, Okayama-Kyoto, Japan, during July and August 1997. Tokyo: Kinokuniya Company Ltd. Adv. Stud. Pure Math. 26, 99-127 (2000).
The paper under review is a nice expository article on the author’s work on discretely decomposable restrictions of unitary representations, which were published in three papers: (i) Invent. Math. 117, 181-205 (1994; Zbl 0826.22015); (ii) Ann. Math. (2) 147, 709-729 (1998; Zbl 0910.22016); (iii) Invent. Math. 131, 229-256 (1998; Zbl 0907.22016). At the end of the paper, a few conjectures are given.
For the entire collection see [Zbl 0941.00016].


22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods