Discrete subgroups of PU(2, 1) with screw parabolic elements
نویسندگان
چکیده
We give a version of Shimizu’s lemma for groups of complex hyperbolic isometries one of whose generators is a parabolic screw motion. Suppose that G is a discrete group containing a parabolic screw motion A and let B be any element of G not fixing the fixed point of A. Our result gives a bound on the radius of the isometric spheres of B and B−1 in terms of the translation lengths of A at their centres. We use this result to give a sub-horospherical region precisely invariant under the stabiliser of the fixed point of A in G.
منابع مشابه
Pinching surface groups in complex hyperbolic plane
We construct first examples of discrete geometrically finite subgroups of PU(2, 1) which contain parabolic elements, and are isomorphic to surface groups of genus ≥ 2.
متن کاملComplex hyperbolic free groups with many parabolic elements
We consider in this work representations of the of the fundamental group of the 3-punctured sphere in PU(2, 1) such that the boundary loops are mapped to PU(2, 1). We provide a system of coordinates on the corresponding representation variety, and analyse more specifically those representations corresponding to subgroups of (3, 3,∞)-groups. In particular we prove that it is possible to construc...
متن کاملPrehomogeneous Spaces for Parabolic Group Actions in Classical Groups
Let G be a reductive linear algebraic group, P a parabolic subgroup of G and Pu its unipotent radical. We consider the adjoint action of P on the Lie algebra pu of Pu. Richardson’s dense orbit theorem says that there is a dense P -orbit in pu. We consider some instances when P acts with a dense orbit on terms p u of the descending central series of pu. In particular, we show (in good characteri...
متن کاملOn Normal Abelian Subgroups in Parabolic Groups
Let G be a reductive algebraic group, P a parabolic subgroup of G with unipotent radical Pu, and A a closed connected unipotent subgroup of Pu which is normalized by P. We show that P acts on A with nitely many orbits provided A is abelian. This generalizes a well-known niteness result, namely the case when A is central in Pu. We also obtain an analogous result for the adjoint action of P on in...
متن کاملS-arithmeticity of Discrete Subgroups Containing Lattices in Horospherical Subgroups
0. Introduction. Let Qp be the field of p-adic numbers, and let Q∞ = R. Let Gp be a connected semisimpleQp-algebraic group. The unipotent radical of a proper parabolic Qp-subgroup of Gp is called a horospherical subgroup. Two horospherical subgroups are called opposite if they are the unipotent radicals of two opposite parabolic subgroups. In [5] and [6], we studied discrete subgroups generated...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004