Related papers: On the wonderful compactification
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
De Concini and Procesi have defined the wonderful compactification of a symmetric space X=G/H with G a semisimple adjoint group and H the subgroup of fixed points of G by an involution s. It is a closed subvariety of a grassmannian of the…
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional…
The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and…
We describe the primitive central idempotents of the group algebra over a number field of finite monomial groups. We give also a description of the Wedderburn decomposition of the group algebra over a number field for finite strongly…
We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not…
In this paper we introduce the notion of weighted (weakly) almost periodic compactifcation of a semitopological semigroup and generalize this notion to corresponding notion for transformation semigroup.The inclusion relation and equality of…
This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.
$p$-Adic compactifications of geometric loop and diffeomorphism groups of compact manifolds on finite-dimensional spaces over non-Archimedean fields are investigated. Weakened topology is introduced. The structure of newly constructed…
Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-sections in real symplectic geometry.
In this paper we construct compact forms associated with a complex Lie supergroup with Lie superalgebra of classical type.
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
We discuss the `hd-compactification' of a semi-simple Lie group to a manifold with corners; it is the real analog of the wonderful compactification of deConcini and Procesi. There is a 1-1 correspondence between the boundary faces of the…
A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.
We give various realizations of the adjoint orbits of a semi-simple Lie group and describe their symplectic geometry. We then use these realizations to identify a family of Lagrangean submanifolds of the orbits.
Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
This work is a PhD thesis. First we provide some general context on wonderful varieties and moduli spaces of rational curves. Working over complex numbers we prove that the moduli space of rational curves with no marked points on the…
Given an adjoint semisimple group $G$ over a local field $k$, we prove that the maximal Satake-Berkovich compactification of the Bruhat-Tits building of $G$ can be identified with the one obtained by embedding the building into the…