Related papers: Cartan-decomposition subgroups of SU(2,n)

For each finite subgroup G of SL(n, C), we introduce the generalized Cartan matrix C_{G} in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices…

In this paper we show that topological subgroupoids of Lie groupoids, under special circumstances are Lie subgroupoids. Giving an example, we indicate that having the same topological dimension is a necessary condition for topological…

Let $G$ be a connected real Lie group with associated Lie algebra $\mathfrak g$, and let ${\rm Aut}(G)$ be the group of (Lie) automorphisms of $G$. It is noted here that, given a super-solvable subgroup $\Gamma\subset {\rm Aut}(G)$ of…

The efficacy of using complexifications to understand the structure of real algebraic groups is demonstrated. In particular the following results are proved: a) If L is an algebraic subgroup of a connected real algebraic group G such that…

We prove that for a compact subgroup $H$ of an almost connected locally compact Hausdorff group $G$, the following properties are mutually equivalent: (1) $H$ is a maximal compact subgroup of $G$, (2) $G/H$ is contractible, (3) $G/H$ is…

Let $K$ be a compact set in the complex plane $\C$, such that its complement in the Riemann sphere, $(\C\cup\{\infty\})\sm K$, is connected. Also, let $U\subseteq\C$ be an open set which contains $K$. Then there exists a simply connected…

Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on G^n, the n-fold Cartesian product of G with itself, by simultaneous conjugation. We give a purely algebraic…

Well-known work of Renault shows that if $\mathcal{E}$ is a twist over a second countable, effective, \'etale groupoid $G$, then there is a naturally associated Cartan subalgebra of the reduced twisted groupoid C*-algebra $C^*_{r}(G; E)$,…

We study the Grassmann manifold $G_k$ of all $k$-dimensional subspaces of ${\mathbb R}^n$. The Cartan embedding $G_k\subset O(n)$ realizes $G_k$ as a subspace of $Sl_n({\mathbb R})$ and we study the decomposition $G_k=\coprod_w (BwB\cap…

We say that a graph $G$ on $n$ vertices is $\{H,F\}$-$o$-heavy if every induced subgraph of $G$ isomorphic to $H$ or $F$ contains two nonadjacent vertices with degree sum at least $n$. Generalizing earlier sufficient forbidden subgraph…

The component size of a graph is the maximum number of edges in any connected component of the graph. Given a graph $G$ and two integers $k$ and $c$, $(k,c)$-Decomposition is the problem of deciding whether $G$ admits an edge partition into…

We prove that groups definable in o-minimal structures have Cartan subgroups, and only finitely many conjugacy classes of such subgroups. We also delineate with precision how these subgroups cover the ambient group, in general very largely…

In this paper, we present a simple proof of the fact that any compact subgroup of homeomorphisms of the 2-sphere is topologically conjugate to a closed subgroup of the orthogonal group O(3).

For a representation of a connected compact Lie group G in a finite dimensional real vector space U and a subspace V of U, invariant under a maximal torus of G, we obtain a sufficient condition for V to meet all G-orbits in U, which is also…

We describe the relation between G-character varieties, $X_G(\Gamma)$, and $G/H$-character varieties, where $H$ is a finite, central subgroup of $G.$ In particular, we find finite generating sets of coordinate rings $C[X_{G/H}(\Gamma)]$ for…

Let $k$ be a positive integer and let $G$ be a graph with $n$ vertices. A connected $k$-subpartition of $G$ is a collection of $k$ pairwise disjoint sets (a.k.a. classes) of vertices in $G$ such that each set induces a connected subgraph.…

It is shown that a flat subgroup, $H$, of the totally disconnected, locally compact group $G$ decomposes into a finite number of subsemigroups on which the scale function is multiplicative. The image, $P$, of a multiplicative semigroup in…

We study the set ${\cal C}$ consisting of pairs of orthogonal projections $P,Q$ acting in a Hilbert space ${\cal H}$ such that $PQ$ is a compact operator. These pairs have a rich geometric structure which we describe here. They are parted…

A real form $G_0$ of a complex semisimple Lie group $G$ has only finitely many orbits in any given compact $G$-homogeneous projective algebraic manifold $Z=G/Q$. A maximal compact subgroup $K_0$ of $G_0$ has special orbits $C$ which are…

We say a graph $H$ decomposes a graph $G$ if there exists a partition of the edges of $G$ into subgraphs isomorphic to $H$. We seek to characterize necessary and sufficient conditions for a cycle of length $k$, denoted $C_k$, to decompose…