Related papers: Positive representations over real closed fields

We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…

We consider (projectively) linearly sofic groups, i.e. groups which can be approximated using (projective) matrices over arbitrary fields, as a generalization of sofic groups. We generalize known results for sofic groups and groups which…

We show that for a fixed k, Gromov random groups with any positive density have no non-trivial degree-k representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when the…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

Preface (A.Vershik) - about these texts (3.); I.Interpolation between inductive and projective limits of finite groups with applicatons to linear groups over finite fields; II.The characters of the groups of almost triangle matrices over…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…

The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…

We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We…

We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group.…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…

We show that certain representations over fields with positive characteristic of groups having CAT(0) fixed point property ${\rm F}\mathcal{B}_{\widetilde{A}_n}$ have finite image. In particular, we obtain rigidity results for…

Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…

We establish an entropy rigidity theorem for Hitchin representations of all geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin representations of closed surface groups. In the process, we…

We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…

We show that for every representation $ \rho : \pi_{1} (S_{g}) \to \text{Isom}(X) $ of the fundamental group of a genus $ g \ge 2 $ surface to the isometry group of a complete $ \text{CAT}(-1) $ metric space $ X $ there exists a Fuchsian…

We study a class of tame $\mathcal{L}$-theories $T$ of topological fields and their $\mathcal{L}_\delta$-extension $T_{\delta}^*$ by a generic derivation $\delta$. The topological fields under consideration include henselian valued fields…

We introduce and develop a categorification of the theory of Real representations of finite groups. In particular, we generalize the categorical character theory of Ganter--Kapranov and Bartlett to the Real setting. Given a Real…