Let X=G/H be a homogeneous space, where G H are reductive Lie groups. We ask: in the setting where Γ\G/H is a standard quotient, to what extent can the discrete subgroup Γ be deformed while preserving the proper discontinuity of the Γ-action on X?We provide several classification results, including: conditions under which local rigidity holds for compact standard quotients Γ\X; criteria for when a standard quotient can be deformed into a nonstandard one; a characterization of the maximal Zariski-closure of discontinuous groups under small deformations; and conditions under which Zariski-dense deformations occur.
Proofs of the results stated in this paper are provided in detail in arXiv:2507.03476.
[ DOI | arXiv | preprint version(pdf) ]
© Toshiyuki Kobayashi