Let P be a parabolic subgroup of a semisimple simply connected linear algebraic group G over C and ρ an irreducible homomorphism from P to a complex reductive group H . We show that the associated principal H –bundle over G/P , associated for ρ to the principal P –bundle defined by the quotient map G −→ G/P , is stable. We describe the Harder–Narasimhan reduction of the G–bundle over G/P obtain...

Let Γ be a torsion free lattice in G = PGL(n+ 1,F), where n ≥ 1 and F is a non-archimedean local field. Then Γ acts on the Furstenberg boundary G/P , where P is a minimal parabolic subgroup of G. The identity element I in the crossed product C∗-algebra C(G/P ) ⋊ Γ generates a class [I] in the K0 group of C(G/P ) ⋊ Γ. It is shown that [I] is a torsion element of K0 and there is an explicit bound...

Abstract. This paper presents a new observability estimate for parabolic equations in × (0, T ), where  is a convex domain. The observation region is restricted over a product set of an open nonempty subset of  and a subset of positive measure in (0, T ). This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property f...

If φ is an analytic selfmap of the disk (not an elliptic automorphism) the DenjoyWolff Theorem predicts the existence of a point p with |p| ≤ 1 such that the iterates φn converge to p uniformly on compact subsets of the disk. Since these iterates are bounded analytic functions, there is a subset of the unit circle of full linear measure where they are all well-defined. We address the question o...

Let G be a (real or complex) semisimple Lie group, whose Lie algebra g is endowed with a so called jkj{grading, i.e. a grading of the form g = g ?k g k , such that no simple factor of G is of type A 1. Let P be the subgroup corresponding to the subalgebra p = g 0 g k. The aim of this paper is to clarify the geometrical meaning of Cartan connections corresponding to the pair (G; P) and to study ...

Abstract. This paper presents a new observability estimate for parabolic equations in × (0, T ), where  is a convex domain. The observation region is restricted over a product set of an open nonempty subset of  and a subset of positive measure in (0, T ). This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property f...

Let M be the moduli space of generalized parabolic bundles (GPBs) of rank r and degree d on a smooth curve X . Let ML̄ be the closure of its subset consisting of GPBs with fixed determinant L̄. We define a moduli functor for which ML̄ is the coarse moduli scheme. Using the correspondence between GPBs on X and torsion-free sheaves on a nodal curve Y of which X is a desingularization, we show that M...

We examine the structure of the Levi component MA in a minimal parabolic subgroup P = MAN of a real reductive Lie group G and work out the cases where M is metabelian, equivalently where p is solvable. When G is a linear group we verify that p is solvable if and only if M is commutative. In the general case M is abelian modulo the center ZG , we indicate the exact structure of M and P , and we ...

Let H and K be spherical subgroups of a reductive complex group G. In many cases, detailed knowledge of the double coset space H\G/K is of fundamental importance in group theory and representation theory. If H or K is parabolic, then H\G/K is finite, and we recall the classification of the double cosets in several important cases. If H = K is a symmetric subgroup of G, then the double coset spa...

Let G be a semisimple real Lie group of non-compact type, K a maximal compact subgroup and S ⊆ G a semigroup with nonempty interior. We consider the ideal boundary ∂∞(G/K) of the associated symmetric space and the flag manifolds G/PΘ . We prove that the asymptotic image ∂∞(Sx0) ⊆ ∂∞(G/K), where x0 ∈ G/K is any given point, is the maximal invariant control set of S in ∂∞(G/K). Moreover there is ...