Induced representations and finite volume homogeneous spaces

Lattice Action on Finite Volume Homogeneous Spaces

Relativities and Homogeneous Spaces I –finite Dimensional Relativity Representations–

Special relativity, the symmetry breakdown in the electroweak standardmodel, and the dichotomy of the spacetime related transformations with theLorentz group, on the one side, and the chargelike transformations with thehypercharge and isospin group, on the other side, are discussed under the com-mon concept of “relativity”. A relativity is defined by classes G/H of a “little”<lb...

Good Representations and Homogeneous Spaces

Remark. The word generic cannot be replaced by all. We show this in Example 6. Theorem 1 is proven first for complex groups then deduced for real groups. It is not known at this time, to the author, whether or not these results hold true for more general algebraic groups. Our proof exploits Weyl’s Unitarian Trick. Before proving this theorem, we present some corollaries to demonstrate its value...

Finite Volume Spaces and Sparsification

We introduce and study finite d-volumes the high dimensional generalization of finite metric spaces. Having developed a suitable combinatorial machinery, we define l1-volumes and show that they contain Euclidean volumes and hypertree volumes. We show that they can approximate any d-volume with O(n) multiplicative distortion. On the other hand, contrary to Bourgain’s theorem for d = 1, there exi...

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...