English

New time-changes of unipotent flows on quotients of Lorentz groups

Dynamical Systems 2021-07-08 v2 Representation Theory

Abstract

We study the cocompact lattices ΓSO(n,1)\Gamma\subset SO(n,1) so that the Laplace-Beltrami operator Δ\Delta on SO(n)\SO(n,1)/ΓSO(n)\backslash SO(n,1)/\Gamma has eigenvalues in (0,1/4)(0,1/4), and then show that there exist time-changes of unipotent flows on SO(n,1)/ΓSO(n,1)/\Gamma that are not measurably conjugate to the unperturbed ones. A main ingredient of the proof is a stronger version of the branching of the complementary series. Combining it with a refinement of the works of Ratner and Flaminio-Forni is adequate for our purpose.

Keywords

Cite

@article{arxiv.2009.06552,
  title  = {New time-changes of unipotent flows on quotients of Lorentz groups},
  author = {Siyuan Tang},
  journal= {arXiv preprint arXiv:2009.06552},
  year   = {2021}
}