Related papers: On intersections of certain partitions of a group …

We consider smooth, complex quasi-projective varieties $U$ which admit a compactification with a boundary which is an arrangement of smooth algebraic hypersurfaces. If the hypersurfaces intersect locally like hyperplanes, and the relative…

Let G be a semi-simple algebraic group over ${\mathbb C}$, B a Borel subgroup of G and T a maximal torus in B. A beautiful unpublished result of Dale Peterson says that if G is simply laced, then every rationally smooth point of a Schubert…

A topological space $G$ is said to be a {\it rectifiable space} provided that there are a surjective homeomorphism $\phi :G\times G\rightarrow G\times G$ and an element $e\in G$ such that $\pi_{1}\circ \phi =\pi_{1}$ and for every $x\in G$…

The spectrum of an admissible subalgebra $\mathscr{A}(G)$ of $\mathscr{LUC}(G)$, the algebra of right uniformly continuous functions on a locally compact group $G$, constitutes a semigroup compactification $G^\mathscr{A}$ of $G$. In this…

Let $G$ be a group. The intersection graph of cyclic subgroups of $G$, denoted by $\mathscr I_c(G)$, is a graph having all the proper cyclic subgroups of $G$ as its vertices and two distinct vertices in $\mathscr I_c(G)$ are adjacent if and…

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

Given a pair of number fields with isomorphic rings of adeles, we construct bijections between objects associated to the pair. For instance we construct an isomorphism of Brauer groups that commutes with restriction. We additionally…

We show that the number of conjugacy classes of intersections $A\cap B^g$, for fixed finitely generated subgroups $A, B<F$ of a free group, is bounded above in terms of the ranks of $A$ and $B$; this confirms an intuition of Walter Neumann.…

Let $G$ be a compact connected Lie group acting on a stable complex manifold $M$ with equivariant vector bundle $E$. Besides, suppose $\phi$ is an equivariant map from $M$ to the Lie algebra $\mathfrak{g}$. We can define some equivalence…

We show, under some natural conditions, that the set of abelian points on the non-anomalous subset of a closed irreducible subvariety $X$ intersected with the union of connected algebraic subgroups of codimension at least $\dim X$ in a…

We say that two unitary or orthogonal representations of a finitely generated group $G$ are additive conjugates if they are intertwined by an additive map, which need not be continuous. We associate to each representation of $G$ a…

We study the GIT compactifications of pairs formed by a hypersurface and a hyperplane. We provide a general setting to characterize all polarizations which give rise to different GIT quotients. Furthermore, we describe a finite set of…

Let $G$ be a locally compact totally disconnected topological group. Under a necessary mild assumption, we show that the irreducible unitary representations of $G$ are uniformly admissible if and only if the irreducible smooth…

Let $\G$ be a semisimple algebraic group defined over a number field $K$, $\te$ a maximal $K$-split torus of $\G$, $\mathcal{S}$ a finite set of valuations of $K$ containing the archimedean ones, $\OO$ the ring of $\mathcal{S}$-integers of…

Let G be a complex reductive algebraic group. We study complete intersections in a spherical homogeneous space G/H defined by a generic collection of sections from G-invariant linear systems. Whenever nonempty, all such complete…

We classify the pairs $(C,G)$ where $C$ is a seminormal curve over an arbitrary field $k$ and $G$ is a smooth connected algebraic group acting faithfully on $C$ with a dense orbit, and we determine the equivariant Picard group of $C$. We…

This paper introduces the notion of orbit coherence in a permutation group. Let $G$ be a group of permutations of a set $\Omega$. Let $\pi(G)$ be the set of partitions of $\Omega$ which arise as the orbit partition of an element of $G$. The…

Consider the moment map $\mu \colon T^*(\mathfrak{p} \times \mathbb{C}^n) \to \mathfrak{p}^*$ for a parabolic subalgebra $\mathfrak{p}$ of $\mathfrak{gl}_n(\mathbb{C})$. We prove that the preimage of $0$ under $\mu$ is a complete…

Let G be a connected semisimple group over a non-Archimedean local field. For every faithful, geometrically irreducible linear representation of G we define a compactification of the associated Bruhat-Tits building X(G). This yields a…

Let $G$ be a quasi-simple algebraic group defined over an algebraically closed field $k$ and $B$ a Borel subgroup of $G$ acting on the nilradical $\mathfrak{n}$ of its Lie algebra $\mathfrak{b}$ via the Adjoint representation. It is known…