Related papers: Approximate Representations and Approximate Homomo…

The representation ring of an affine algebraic group scheme can be endowed with the structure of a (special) $\lambda$-ring. We show that the same is true for the ring of symmetric representations, i.e. for the Grothendieck-Witt ring of the…

Let $ f_0 $ and $ f_\infty $ be formal power series at the origin and infinity, and $ P_n/Q_n $, with $ \mathrm{deg}(P_n),\mathrm{deg}(Q_n)\leq n $, be a rational function that simultaneously interpolates $ f_0 $ at the origin with order $…

We investigate the classes of functions whose minimization diagrams can be approximated efficiently in \Re^d. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions.…

We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

The equational probabilistic spectrum of a finite algebra is the set of probabilities with which equations are satisfied in the algebra. We study algebras with minimal spectrum, that is, spectra consisting only of the values $1$ and…

We prove various finiteness and representability results for cohomology of finite flat abelian group schemes. In particular, we show that if $f\colon X\rightarrow \mathrm{Spec}(k)$ is a projective scheme over a field $k$ and $G$ is a finite…

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a…

We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…

The chief aim of this paper is to describe a procedure which, given a $d$-dimensional absolutely irreducible matrix representation of a finite group over a finite field $\mathbb{E}$, produces an equivalent representation such that all…

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

Whittaker functions are special functions that arise in $p$-adic number theory and representation theory. They may be defined on representations of reductive groups as well as their metaplectic covering groups: fascinatingly, many of their…

The representation complexity of a bipartite graph $G=(P,Q)$ is the minimum size $\sum_{i=1}^s (|A_i|+|B_i|)$ over all possible ways to write $G$ as a (not necessarily disjoint) union of complete bipartite subgraphs $G=\cup_{i=1}^s…

In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions,…

We consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part, $H_{\text{adfin}}$, defined as the sum of all finite-dimensional subrepresentations. For virtually cocommutative $H$ (i.e., $H$ is finitely…

Function fitting/approximation plays a fundamental role in computer graphics and other engineering applications. While recent advances have explored neural networks to address this task, these methods often rely on architectures with many…

The paper concerns algebras of almost periodic pseudodifferential operators on $\mathbb R^d$ with symbols in H\"ormander classes. We study three representations of such algebras, one of which was introduced by Coburn, Moyer and Singer and…

Let $G$ be a connected Lie group, $C$ be the maximal compact connected subgroup of the center of $G$, and let Aut$(G)$ denote the group of Lie automorphisms of $G$, viewed, canonically, also as a subgroup of GL$(\frak G)$, where $\frak G$…

We consider the problem of finding for a given $N$-tuple of polynomials (real or complex) the closest $N$-tuple that has a common divisor of degree at least $d$. Extended weighted Euclidean seminorm of the coefficients is used as a measure…

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…