On the classification of k-involutions I (2008)
Abstract. Let G be a connected reductive algebraic group defined over a field k of characteristic not 2, θ an involution of G defined over k, H a k-open subgroup of the fixed point group of θ and...
ALGORITHMS FOR TWISTED INVOLUTIONS IN WEYL GROUPS (2008)
Abstract. Let (W, Σ) be a finite Coxeter system, and θ an involution such that θ(∆) = ∆, where ∆ is a basis for the root system Φ associated with W, and Iθ = {w ∈ W | θ(w) = w −1} the...
On the classification of symmetric k-varieties I (2008)
Abstract. Let G be a connected reductive algebraic group defined over a field k of characteristic not 2, θ an involution of G defined over k, H a k-open subgroup of the fixed point group of θ and...
A conjugacy theorem for symmetric spaces (2007)
A. G Helminck, J. Hilgert, A. Neumann, G. Ólafsson
Abstract. In this paper we prove that two Cartan subspaces of a semisimple symmetric pair (�,τ)are conjugate under G = Int(�) if and only if they are conjugate under (G τ) 0. Moreover we derive...
Computing B-Orbits On G/H (2007)
. The orbits of a Borel subgroup acting on a symmetric variety G/H occur in several areas of mathematics. For example, these orbits and their closures are essential in the study of Harish Chandra...
Computing Orbits Of Minimal Parabolic k-Subgroups Acting On Symmetric k-Varieties (2007)
. The orbits of a minimal parabolic k-subgroup acting on a symmetric k-variety are essential to the study of symmetric k-varieties and their representations. This paper gives an algorithm to compute...
Computing admissible sequences for twisted involutions in Weyl groups (2004)
Abstract. Let (W, �) be a finite Coxeter system, and θ an involution such that θ(�) = �, where � is a basis for the root system � associated with W. We show that the set of θ-twisted...
Spherical distribution vectors (2002)
Helminck, A.G., Helminck, G.F.
In this paper we consider a locally compact second countable unimodular group $G$ and a closed unimodular subgroup $H$. Let $\rho$ be a finite dimensional unitary representation of $H$ with closed...
Helminck, G.F., Helminck, A.G.
In this paper one considers a unimodular second countable locally compact group $G$ and the homogeneous space $X:=H /G$, where $H$ is a closed unimodular subgroup of $G$. Over $X$ complex vector...
Hilbert flag varieties and their K\"{a}hler structure (2002)
Helminck, G.F., Helminck, A.G.
In this paper we introduce the infinite-dimensional flag varieties associated with integrable systems of the $KdV$- and $Toda$-type and we discuss the structure of these manifolds. As an example we...
A Conjugacy Theorem For Symmetric Spaces (1998)
A.G. Helminck, J. Hilgert, A. Neumann, G. Olafsson
. In this paper we prove that two Cartan subspaces of a semisimple symmetric pair (g; ø) are conjugate under G = Int(g) if and only if they are conjugate under (G ø ) 0 . Moreover we derive a...
Tori Invariant Under An Involutorial Automorphism II (1997)
. The geometry of the orbits of a minimal parabolic k-subgroup acting on a symmetric k-variety is essential in several area's, but its main importance is in the study of the representations...
On Rationality Properties Of Involutions Of Reductive Groups (1993)
A.G. Helminck, A. G. Helminck, S. P. Wang, S. P. Wang
this paper were announced in [12]