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The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
The method of nonlinear realizations is applied for the conformally invariant description of the spinning particles in terms of geometrical quantities of the parameter spaces of the one dimensional N - extended superconformal groups. We…
A superparticle action which is globally supersymmetric in the target space is proposed. The supersymmetry is the supersymmetric extension of the rotation group O(3).
The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of…
This paper introduces the idea of pseudo-group. Applications of pseudo-groups in Group Theory and Symmetry Breaking in Particle Physics and Cosmology are considered.
We present a short overview of the structure and couplings of supergravity theories at the component level. We do so with as little technical machinery as possible, working directly with the physical on-shell fields and using explicit…
This article reviews the subject of supersymmetry and its breaking. The emphasis is on recent developments in metastable, dynamical supersymmetry breaking, which permit the construction of promising models of particle physics.
We give a brief overview of 20 open theoretical questions in supersymmetric particle physics. The 20 questions we have chosen range from the GeV scale to the Planck scale, and include issues pertaining to the Minimal Supersymmetric Standard…
We briefly cover the early history of supersymmetry, describe the relation of SUSY quantum field theories to superstring theories and explain why they are considered a likely tool to describe the phenomenology of high energy particle theory…
In this work we investigate connections between superalgebras and their realizations in terms of particles, branes and field theory models. We start from Poincar\'e superalgebras with brane charges and study its representations. The…
We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial…
Some aspects of the geometry of superembeddings and its application to supersymmetric extended objects are discussed. In particular, the embeddings of (3|16) and (6|16) dimensional superspaces into (11|32) dimensional superspace,…
The classical (1,0) superparticle in a curved superspace is considered. The minimal set of constraints to be imposed on the background for correct inclusion of interaction is found. The most general form of Siegel-type local fermionic…
The article is devoted to linear quasigroups and some of their generalizations. In the first part main definitions and notions of the theory of quasigroups are given. In the second part some elementary properties of linear quasigroups and…
Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups…
This paper introduces new structural decompositions for almost symmetric numerical semigroups through the combinatorial lens of Young diagrams. To do that, we use the foundational correspondence between numerical sets and Young diagrams,…
Classical results and recent developments on the theoretical description of elementary particles with "continuous" spin are reviewed. At free level, these fields are described by unitary irreducible representations of the isometry group…
In this paper, we investigate some characteristic features of holomorphic semigroups. In particular, we investigate nice examples of holomorphic semigroups whose every left or right ideal includes minimal ideal. These examples are compact…
A super-modular category is a unitary pre-modular category with M\"uger center equivalent to the symmetric unitary category of super-vector spaces. Super-modular categories are important alternatives to modular categories as any unitary…
We give a thorough structural analysis of the principal one-sided ideals of arbitrary semigroups, and then apply this to full transformation semigroups and symmetric inverse monoids. One-sided ideals of these semigroups naturally occur as…