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In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We give various ext...
Several large classes of homogeneous spaces are known to be formal---in the sense of Rational Homotopy Theory. However, it seems that far fewer examples of non-formal homogeneous spaces are known.
Abstract: We study the smooth untwisted cohomology with real coefficients for the action on [SL(2, R) \times \cdot \cdot \cdot \times SL(2, R)]/{\Gamma} by the subgroup of diagonal matrices, where {\G...
Abstract: Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. Using the dual Ramsey theorem and a detailed combinatorial analysi...
Abstract: An answer to the question: Can, in general, the adoption of a given symmetry induce a further symmetry, which might be hidden at a first level? has been attempted in the context of different...
For geometries with a closed three-form we briefly overview the notion of multimoment maps. We then give concrete examples of multi-moment maps for homogeneous hypercomplex and nearly K¨ahler manifold...
Let X be a homogeneous space, X = G/H, where G is a connected linear algebraic group over a number field k, and H  G is a k-subgroup (not necessarily con-nected). Let S be a finite set of places of k...
In this paper, we quantize universal gauge groups such as SU(∞), as well as their homogeneous spaces, in the -C-algebra setting.
The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the repre-sentations of G on the spaces of regular sections of homogen...
Vacuum expectation value of the stress-energy-momentum tensor for scalar and spinor fields is obtainted on the homogeneous space with G-invariant metrics using the orbits of coadjoint representation o...
In this article, assume that G=H\timest K is the semidirect product of two locally compact groups H and K, respectively and consider the quasi regular representation on G. Then for some closed subgrou...
We prove the three embeddedness results as follows. $({\rm i})$ Let $\Gamma_{2m+1}$ be a piecewise geodesic Jordan curve with $2m+1$ vertices in $\mathbb{R}^n$, where $m$ is an integer $\geq2$. Then t...
The theorems in Drinfel′d (1993), Liu et al. (1998), Jotz (2010a) about one-one orrespondence between homogeneous objects of a Poisson Lie group (respectively Poisson Lie groupoid, Dirac Lie group)and...
It is well-known that for a surface in a 3-dimensional real space form the constancy of the mean curvature is equivalent to the harmonicity of the Gauss map. However, this is not true in general for...

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