Related papers: On the wonderful compactification
We discuss some notions of compactness and convergence relative to a specified family F of subsets of some topological space X. The two most interesting particular cases of our construction appear to be the following ones. (1) The case in…
In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.
We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly…
These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
We describe the $G$-equivariant Grothendieck ring of a regular compactification $X$ of an adjoint symmetric space $G/H$ of minimal rank. This extends the results of Brion and Joshua for the equivariant Chow ring of wonderful symmetric…
Every topological group $G$ has some natural compactifications which can be a useful tool of studying $G$. We discuss the following constructions: (1) the greatest ambit $S(G)$ is the compactification corresponding to the algebra of all…
The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.
Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.
The given study uses the methods to identify compactifications of semigroups $S\subset L(X),$ which reside in the space $L(X).$ This method generalizes in some sense the deLeeuw-Glicksberg-Theory to a greater class of functions. The…
A class of Cantor-type spaces and related geometric structures are discussed.
A recent theorem of [GGSM1] showed that adjoint orbits of semisimple Lie algebras have the structure of symplectic Lefschetz fibrations. We investigate the behaviour of their fibrewise compactifications. Expressing adjoint orbits and fibres…
Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general…
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…
We investigate the topology of the closure in a wonderful compactification of the set of unipotent-invariant bilinear forms.
We extend the homotopy theories based on point reduction for finite spaces and simplicial complexes to finite acyclic categories and $\Delta$-complexes, respectively. The functors of classifying spaces and face posets are compatible with…
We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over…
In these lectures we review the motivation, principles of and (circumstantial) evidence for the program of unification of the fundamental forces. In an appendix, we review the group theory pertinent to the program.
Let X be the wonderful compactification of a semisimple adjoint algebraic group. Extending the standard monomials on the flag variety, Chirivi and Maffei constructed a basis of the space of global sections on X that is compatible with all…
In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.