Calculating Cartan spaces for affine homogeneous spaces

Computation of the Cartan Spaces of Affine Homogeneous Spaces

Let G be a reductive algebraic group and H its reductive subgroup. Fix a Borel subgroup B ⊂ G and a maximal torus T ⊂ B. The Cartan space aG,G/H is, by definition, the subspace of Lie(T )∗ generated by the weights of B-semiinvariant rational functions on G/H . We compute the spaces aG,G/H.

Affine Embeddings of Homogeneous Spaces

Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneous space G/H admits an affine embedding if and only if G/H is a quasi-affine algebraic variety. We start with some basic properties of affine embeddings and consider the cases, where the theory is well-de...

Zero - Entropy Affine Maps on Homogeneous Spaces

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