Related papers: Approximate Representations and Approximate Homomo…

The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothendieck ring of the category of finitely generated…

This is the second of a pair of papers on extended geometrically finite (EGF) representations, which were originally posted as a single article under the title "An extended definition of Anosov representation for relatively hyperbolic…

In this paper we use the quantization of fields based on Geometric Langlands Correspondence \cite{diep1} to realize the automorphic representations of some concrete series of groups: for the affine Heisenberg (loop) groups it is reduced to…

Let $\mathbb{F}$ be a field and $\mathsf{G}$ a group. This work is inspired in the following problem: "{\it given a division (simple) $\mathsf{G}$-graded $\mathbb{F}$-algebra, is there any other division (simple) $\mathsf{G}$-graded…

In this paper, the 2-category $\mathfrak{Rep}_{{\bf 2Mat}_{\mathbb{C}}}(\mathbb{G})$ of (weak) representations of an arbitrary (weak) 2-group $\mathbb{G}$ on (some version of) Kapranov and Voevodsky's 2-category of (complex) 2-vector spaces…

In this thesis we study the following property of a finite group G: the minimal number n such that G embeds in Sn. We start with an explicit formula for the number n for abelian groups. Then, we study the behavior of this group property in…

We study stability of metric approximations of countable groups with respect to groups endowed with ultrametrics, the main case study being a $p$-adic analogue of Ulam stability, where we take $GL_n(\mathbb{Z}_p)$ as approximating groups…

A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…

We introduce and discuss a definition of approximation of a topological algebraic system $A$ by finite algebraic systems of some class $\K$. For the case of a discrete algebraic system this definition is equivalent to the well-known…

A global representation is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups $\mathscr{U}$. Global representations assemble into an abelian category…

We study some geometric properties of actions on nonpositively curved spaces related to complete reducibility and semisimplicity, focusing on representations of a finitely generated group in the group G of rational points of a reductive…

We show that for a finite group $G$, the commuting probability of $G$ can be explicitly bounded from below in a nontrivial way by a function in the maximum fraction of elements inverted resp. squared by an automorphism of $G$. Using these…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

Let $\mathbb{F}_{q}$ be a finite field of characteristic $p$, and let $W_{2}(\mathbb{F}_{q})$ be the ring of Witt vectors of length two over $\mathbb{F}_{q}$. We prove that for any reductive group scheme $\mathbb{G}$ over $\mathbb{Z}$ such…

For a finite group $G$, let $\text{rdim}(G)$ denote the smallest dimension of a faithful, complex linear representation of $G$. It is clear that $\text{rdim}(H)\leq \text{rdim}(G)$ for any subgroup $H$ of $G$. We consider $G$ with the…

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that…

In this paper, we construct and study derived character maps of finite-dimensional representations of $\infty$-groups. As models for $\infty$-groups we take homotopy simplicial groups, i.e. homotopy simplicial algebras over the algebraic…

Following the success of the so-called algebraic approach to the study of decision constraint satisfaction problems (CSPs), exact optimization of valued CSPs, and most recently promise CSPs, we propose an algebraic framework for valued…

Approximate morphisms have seen significant study across many areas of mathematics, for instance, in the theory of Absolute (Neighborhood) Retracts in topology, or of almost-commuting unitary matrices in analysis. This paper initiates study…

This paper is a significant contribution to a general programme aimed to classify all projective irreducible representations of finite simple groups over an algebraically closed field, in which the image of at least one element is…