Related papers: Representation equivalent Bieberbach groups and st…

Given a quantum graph $ \Gamma $, a finite symmetry group $ G $ acting on it and a representation $ R $ of $ G $, the quotient quantum graph $ \Gamma /R $ is described and constructed in the literature [1, 2, 18]. In particular, it was…

There is a well known bijective correspondence between isomorphism classes of polystable vector bundles $E$ with $c_i(E)=0$ for $i\geq 1$ on a smooth complex projective variety and equivalence classes of unitary representations of the…

We characterize those unipotent representations of the fundamental group $\pi_1(X,x)$ of a compact Kaehler manifold $X$, which correspond to a Higgs bundle whose underlying Higgs field is equal to zero. The characterization is parallel to…

Let $G$ be a metric group and let $\sA ut(G)$ denote the automorphism group of $G$. If $\sA$ and $\sB$ are groups of $G$-valued maps defined on the sets $X$ and $Y$, respectively, we say that $\sA$ and $\sB$ are \emph{equivalent} if there…

Let $\Gamma$ be a finitely generated group which is hyperbolic relative to a finite family $\{H_1,...,H_n\}$ of subgroups. We prove that $\Gamma$ is uniformly embeddable in a Hilbert space if and only if each subgroup $H_i$ is uniformly…

Let $\Gamma$ be a finitely presented group and $G$ a linear algebraic group over $\mathbb{R}$. A representation $\rho:\Gamma\rightarrow G(\mathbb{R})$ can be seen as an $\mathbb{R}$-point of the representation variety $\mathfrak{R}(\Gamma,…

If a geometry $\Gamma$ is isomorphic to the residue of a point $A$ of a shadow geometry of a spherical building $\Delta$, a representation $\varepsilon_\Delta^A$ of $\Gamma$ can be given in the unipotent radical $U_{A^*}$ of the stabilizer…

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement…

We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or the total space of an orbifiber bundle over $\mathbb{S}^1$…

We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably…

Given a finite group $G$, the generating graph $\Gamma(G)$ of $G$ has as vertices the non-identity elements of $G$ and two vertices are adjacent if and only if they are distinct and generate $G$ as group elements. Let $G$ be a 2-generated…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

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…

For any natural number $n$, the group $G_n$ of all invertible affine transformations of $n$-dimensional Euclidean space has, up to equivalence, just one square-integrable representation and the left regular representation of $G_n$ is a…

If M is a manifold with an action of a group G, then the homology group H_1(M,Q) is naturally a Q[G]-module, where Q[G] denotes the rational group ring. We prove that for every finite group G, and for every Q[G]-module V, there exists a…

Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper, we give a nearly complete classification of such groups for…

Orbifold groupoids have been recently widely used to represent both effective and ineffective orbifolds. We show that every orbifold groupoid can be faithfully represented on a continuous family of finite dimensional Hilbert spaces. As a…

A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold that is locally modeled on $R^n$ modulo the action of a finite group. Orbifolds have proven interesting in a variety of settings. Spectral geometers have…

As a consequence of Kirchberg's work, Connes' Embedding Conjecture is equivalent to the property that every homomorphism of the group $F_\infty\times F_\infty$ into the unitary group $U(\ell^2)$ with the strong topology is pointwise…

We define $G$-cospectrality of two $G$-gain graphs $(\Gamma,\psi)$ and $(\Gamma',\psi')$, proving that it is a switching isomorphism invariant. When $G$ is a finite group, we prove that $G$-cospectrality is equivalent to cospectrality with…