Restriction of small discrete series representations to symmetric subgroups. (English) Zbl 0960.22008

Gross, B.; Wallach, N.

Doran, Robert S. (ed.) et al., The mathematical legacy of Harish-Chandra. A celebration of representation theory and harmonic analysis. Proceedings of an AMS special session honoring the memory of Harish-Chandra, Baltimore, MD, USA, January 9-10, 1998. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 68, 255-272 (2000).

The main ideas of this paper can be divided into three parts: (1) to introduce the notion of small discrete series and to prove their basic properties; (2) to reduce the conjecture of Gross and Prasad to a combinatorial branching formula in case we restrict small discrete series from \(SO(2p, 2q+1)\) to \(SO(2p, 2q)\); (3) to prove a general branching formula that implies reductions.
For the entire collection see [Zbl 0943.00049].

Reviewer: Constantin Udrişte (Bucureşti)

MSC:

22E41	Continuous cohomology of Lie groups
22E45	Representations of Lie and linear algebraic groups over real fields: analytic methods
22E46	Semisimple Lie groups and their representations
22E47	Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)

Keywords:

Weil group; Langlands parameter; semisimple Lie groups; small discrete series; combinatorial branching formula