We study K-orbits in G/P where G is a complex connected reductive group, P ⊆ G is a parabolic subgroup, and K ⊆ G is the fixed point subgroup of an involutive automorphism θ. Generalizing work of Springer, we parametrize the (finite) orbit set K\G/P and we determine the isotropy groups. As a consequence, we describe the closed (resp. affine) orbits in terms of θ-stable (resp. θ-split) parabolic...

Field observations carried out in the Neuse RiverPamlico Sound Estuarine System (NRE-PS), North Carolina, USA were used to develop optical algorithms for assessing inherent optical properties, IOPs (absorption and backscattering) associated with water quality components (WQC). WQCs including chlorophyll a (Chl), volatile (organic) suspended solids (VSS), fixed (inorganic) suspended solids (FSS)...

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...

The effects of norepinephrine-induced vasoconstriction on pulmonary extravascular water volume (PEWV) and central volume were studied before and after intravenous volume expansion with 5% dextrose and water (20 ml/kg body weight). PEWV was measured by double isotope dilution and gravimetric analysis and assessed by electron photomicrography. Comparisons were made with saline-treated control dog...

be found in all classical books on the subject (for example in [4, 44]). For every x ∈ X the isotropy subgroup (also termed fixer or stabilizer) of x is Gx = {g ∈ G : gx = x}. If H ⊂ G is a subgroup of G, then the space fixed by H in X is X = {x ∈ X : Hx = x} = {x ∈ X : H ⊂ Gx}. If X and Y are G-spaces, then a G-map (i.e. an equivariant map) f : X → Y is a map which commutes with the G-action: ...

For real numbers C, T 1 , T 2 , ... we find all solutions µ to the stochastic fixed point equation W j≥1 T j W j + C, where W, W 1 , W 2 , ... are independent real-valued random variables with distribution µ and means equality in distribution. All solutions are infinitely divisible. The set of solutions depends on the closed multiplicative subgroup of R * = R\{0} generated by the T j. If this g...

We will drop the compactness hypothesis on G in the results of §6, doing this in such a way that problems can be reduced to the compact case. This involves the notions of reductive Lie groups and algebras and Cartan involutions. Let © be a Lie algebra. A subalgebra S c © is called a reductive subaU gebra if the representation ad%\® of ίΐ on © is fully reducible. © is called reductive if it is a...

Let F = (E, p, B;Y ) be a fiber bundle where E, B and Y are connected finite polyhedra. Let f : E → E be a fiber-preserving map and A ⊆ E a closed, locally contractible subset. We present necessary and sufficient conditions for A and its subsets to be the fixed point sets of maps fiber-homotopic to f . The necessary conditions correspond to those introduced by Schirmer in 1990 but, in the fiber...

Preface A famous theorem by Frobenius in 1901 proves that if a group G contains a proper non trivial subgroup H such that H ∩ g −1 Hg = {1 G } for all g ∈ G \ H, then there exists a normal subgroup N such that G is the semidirect product of N and H. Groups with this property-the so called Frobenius groups-arise in a natural way as transitive permutation groups, but they can also be characterize...

The certification of Standard Reference Material (SRM is a registered trademark of NIST) 3103a As Spectrometric Solution is based on the gravimetric preparation value that is verified by inductively coupled plasma optical emission spectrometry (ICP-OES) measurements. A disagreement between the gravimetric and the spectrometric values for a batch of As calibration solutions led to the discovery ...