Relative Kazhdan Property

Abstract

We perform a systematic investigation of Kazhdan's relative Property (T) for pairs (G,X), where G a locally compact group and X is any subset. When G is a connected Lie group or a p-adic algebraic group, we provide an explicit characterization of subsets X of G such that (G,X) has relative Property (T). In order to extend this characterization to lattices of G, a notion of "resolutions" is introduced, and various characterizations of it are given. Special attention is paid to subgroups of SU(2,1) and SO(4,1).

36 pages, no figure; to appear in Ann. Sci. Ecole Norm. Sup

Cited by in corpus (6)

• Property $(T)$ for noncommutative universal lattices
• Relative expanders
• On equivariant embeddings of generalized Baumslag-Solitar groups
• Irreducible lattices, invariant means, and commensurating actions
• A characterization of relative Kazhdan Property T for semidirect products with abelian groups
• Rigidity for group actions on homogeneous spaces by affine transformations