Related papers: Adinkras: A Graphical Technology for Supersymmetri…
In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras. This method, which proves to be very powerful, can be applied to most algebras and superalgebras, however. It allows: to…
This is an expanded version of my Shaw Prize Lecture delivered at the Chinese University of Hong Kong.
We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of…
Using graph theory based on Adinkras, we consider once again the study of extremal black branes in the framework of quantum information. More precisely, we propose a one to one correspondence between qubit systems, Adinkras and certain…
A superfield formalism for quantum fields with N-extended superconformal symmetry is developed using vertex algebra techniques in four dimensions.
A re-imagining of the supergravity prepotential formulation of 4D, $\cal N$ = 1 supergravity and its Salam-Strathdee superfield superconformal gauge group is presented.
We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain a symbolic summation framework that solves this problem for sums defined, e.g., over…
We consider a supersymmetric extension of the algebra associated with three and four dimensional Anti de Sitter space. A representation of the supersymmetry operators in superspace is given. Supersymmetry invariant models are constructed…
We discuss a 1+2 dimensional model with unconventional supersymmetry at the boundary of an AdS${}_4$, \,$\mathcal{N}$-extended supergravity. The resulting features of the supersymmetric boundary open the possibility of describing the…
Achieving disentangled representations of information is one of the key goals of deep network based machine learning system. Recently there are more discussions on this issue. In this paper, by comparing the geometric structure of…
An off-shell representation of supersymmetry is a representation of the super Poincare algebra on a dynamically unconstrained space of fields. We describe such representations formally, in terms of the fields and their spacetime…
There is a connection between *-representations of algebras associated with graphs and the problem about the spectrum of a sum of Hermitian operators (spectral problem). For algebras associated with extended Dynkin graphs we give an…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
Using that the dicyclic group is the type D subgroup of SU(2), we extend the Temperley-Lieb diagrammatics to give a diagrammatic presentation of the complex representation theory of the dicyclic group.
This paper studies silted algebras, namely, endomorphism algebras of 2-term silting complexes, over path algebras of Dynkin quivers. We will describe an algorithm to produce all basic 2-term silting complexes over the path algebra of a…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
We introduce a new approach to representation theory of finite groups that uses some basic algebraic geometry and allows to do all the theory without using characters. With this approach, to any finite group $G$ we associate a finite number…
These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…
This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for implementation in stochastic, emerging…