Quantizing Euclidean Motions via Double-Coset Decomposition

Group Decomposition by Double Coset Matrices

A generalized Cartan decomposition for the double coset space

Motivated by recent developments on visible actions on complex manifolds, we raise a question whether or not the multiplication of three subgroups L, G and H surjects a Lie group G in the setting that G/H carries a complex structure and contains G/G ∩ H as a totally real submanifold. Particularly important cases are when G/L and G/H are generalized flag varieties, and we classify pairs of Levi ...

Representations of Double Coset Lie Hypergroups

We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.

Coset and double-coset decompositions of the magnetic point groups.

The coset and double-coset decompositions of the 420 subgroups of m(z)3(xyz)m(xy)1' (O(h)1') and the 236 subgroups of 6(z)/m(z)m(x)m(1)1' (D(6h)1') with respect to each of their subgroups are calculated along with additional mathematical properties of these groups.

Extension of De Rham Decomposition Theorem via Non-euclidean Development

In the present paper, we give a necessary and sufficient condition for a Riemannian manifold (M, g) to have a reducible action of a hyperbolic analogue of the holonomy group. This condition amounts to a decomposition of (M, g) as a warped product of a special form, in analogy to the classical de Rham decomposition theorem for Riemannian manifolds. As a consequence of these results and Berger’s ...