Related papers: On mapping class groups and their TQFT representat…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
In this work, we introduce {\em topological representations of a quiver} as a system consisting of topological spaces and its relationships determined by the quiver. Such a setting gives a natural connection between topological…
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…
We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in…
The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.
The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.
Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…
In this note we prove that the mapping class group of a compact topological manifold $M$ with boundary is of finite type, under assumptions on its dimension and connectivity.
Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…
We construct certain orbifold compactifications of the moduli stack of pointed stable curves over $\mathbb C$ and study their fundamental groups by means of their quantum representations. This enables to construct interesting K\"ahler…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
We study low-dimensional representations of matrix groups over general rings, by considering group actions on CAT(0) spaces, spheres and acyclic manifolds.
Based on different views on the Jones polynomial we review representation theoretic categorified link and tangle invariants. We unify them in a common combinatorial framework and connect them via the theory of Soergel bimodules. The…
The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.
This paper reviews recent results and open problems on the conductor of finite group characters, highlighting their connections to one another and to broader topics in the representation theory of finite groups.
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners to a linear category, generalizing 2d…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…