×

zbMATH — the first resource for mathematics

Branching problems of unitary representations. (English) Zbl 1008.43009
Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press. 615-627 (2002).
Basic theory and new perspectives of admissible restrictions are presented from both the analytic and the algebraic point of view, such as:
1. Admissible restrictions to subgroups, including a criterion for admissible restrictions and its converse statement;
2. infinitesimal discrete decomposability, including a discrete branching law, a criterion for discrete decomposability and the size of irreducible summands;
3. some applications to representation theory;
4. new discrete series for homogeneous spaces, nonsymmetric spaces, symmetric spaces and an exclusive law of discrete spectrum for restriction and induction;
5. modular varieties and vanishing theorems, including vanishing theorems for modular symbols.
For the entire collection see [Zbl 0993.00022].
Reviewer: Su Weiyi (Nanjing)

MSC:
43A85 Harmonic analysis on homogeneous spaces
22E46 Semisimple Lie groups and their representations
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53D20 Momentum maps; symplectic reduction
PDF BibTeX XML Cite
Full Text: arXiv