Related papers: Fusion systems in representation theory
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to…
The methods developed by authors are applied to some reductions of BBGKY hierarchy, namely, various examples of Vlasov-like systems which are important both for fusion modeling and for particular physical problems related to plasma/beam…
Description of system containing classical and quantum subsystems by means of tomographic probability distributions is considered. Evolution equation of the system states is studied.
A proper fusion of complex data is of interest to many researchers in diverse fields, including computational statistics, computational geometry, bioinformatics, machine learning, pattern recognition, quality management, engineering,…
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
In this survey article we summarize the current state of research in representation stability theory. We look at three different, yet related, approaches, using (1) the category of FI-modules, (2) Schur-Weyl duality, and (3)…
We define here two new classes of saturated fusion systems, reduced fusion systems and tame fusion systems. These are motivated by our attempts to better understand and search for exotic fusion systems: fusion systems which are not the…
An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set…
We review several problems of conventional Grand Unification and some new approaches. In particular, we discuss strongly coupled Grand Unified Theories. Standard Model may emerge as a low energy effective theory of composite particles in…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
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 show that every (not necessarily saturated) fusion system can be realized as a full subcategory of the fusion system of a finite group. This result extends our previous work \cite{Park2010} and complements the related result…
We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
This is a revision of some expository lecture notes written originally for a 5-hour minicourse on the intersection theory of punctured holomorphic curves and its applications in 3-dimensional contact topology. The main lectures are aimed…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…
We describe all fusion subcategories of the representation category of a twisted quantum double of a finite group. In view of the fact that every group-theoretical braided fusion category can be embedded into a representation category of a…
These lecture notes were created for a graduate-level course on quantum simulation taught at Leibniz University Hannover in 2013. The first part of the course discusses various state of the art methods for the numerical description of…
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…