Abstract In this paper, we introduce a generalization of G-opers for arbitrary parabolic subgroups P G complex semisimple Lie group. For associated to “even nilpotents”, parameterize ( , ) -opers by an object generalizing the base Hitchin fibration. particular, describe and families opers higher Teichmuller spaces.

A non-elementary Möbius group generated by twoparabolics is determined up to conjugation by one complex parameter and the parameter space has been extensively studied. In this paper, we use the results of [7] to obtain an additional structure for the parameter space, which we term the two-parabolic space. This structure allows us to identify groups that contain additional conjugacy classes of p...

Abstract We show that a group is hyperbolic relative to strongly shortcut groups itself shortcut, thus obtaining new examples of groups. The proof relies on result independent interest: we every relatively acts properly and cocompactly graph in which the parabolic subgroups act convex subgraphs.

Let G be a connected reductive algebraic group defined over a field k of characteristic not 2, σ an involution of G defined over k, H a k-open subgroup of the fixed point group of σ, Gk (resp. Hk) the set of k-rational points of G (resp. H) and Gk/Hk the corresponding symmetric k-variety. A representation induced from a parabolic k-subgroup of G generically contributes to the Plancherel decompo...

We compute the irreducible constituents of the restrictions of all unipotent characters of the groups Sp4(q) and Sp6(q) and odd q to their maximal parabolic subgroups stabilizing a line. It turns out that these restrictions are multiplicity free. We also obtain general information about the restrictions of Harish-Chandra induced characters.

If a group is relatively hyperbolic, the parabolic subgroups are virtually nilpotent if and only if there exists a hyperbolic space with bounded geometry on which it acts geometrically finitely. This provides, via the embedding theorem of M. Bonk and O. Schramm, a very short proof of the finiteness of asymptotic dimension for such groups (which is known to imply Novikov conjectures).

A subgroup H of a group G is conjugately dense in G if for each element g in G the intersection of H with the conjugates of g in G is nonempty. Conjugately dense subgroups deal with interesting open problems, related to parabolic groups. In the present paper we study them with respect to suitable coverings. 2000 Mathematics Subject Classification: 20E45, 20B35, 20F99.