Parallelizability of homogeneous spaces, II

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

The Defect of Weak Approximation for Homogeneous Spaces. Ii

Let X be a right homogeneous space of a connected linear algebraic group G′ over a number field k, containing a k-point x. Assume that the stabilizer of x in G′ is connected. Using the notion of a quasitrivial group, recently introduced by Colliot-Thélène, we can represent X in the form X = H\G, where G is a quasi-trivial k-group and H ⊂ G is a connected k-subgroup. Let S be a finite set of pla...

Stationary Measures and Invariant Subsets of Homogeneous Spaces (ii)

We recall that a probability measure ν on X is said to be μ-stationary if one has μ ∗ ν = ν. It is then said to be μ-ergodic if it is extremal among μ-stationary probability measures. We will say that a probability measure ν on X is homogeneous if it is supported by a closed orbit F of its stabilizer Gν := {g ∈ G | g∗ν = ν}. Such a probability is a finite average of probability measures which a...

Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries

We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes to multiples of Schubert classes. This can be stated as a strange duality property for the Gromov-Witten invariants, which turn out to be very symmetric.