Related papers: Ultradiscrete Soliton Systems and Combinatorial Re…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

This is a tutorial introduction to the representation theory of SU(2) with emphasis on the occurrence of Jacobi polynomials in the matrix elements of the irreducible representations. The last section traces the history of the insight that…

We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.

This paper is about the combinatorics of finite point configurations in the tropical projective space or, dually, of arrangements of finitely many tropical hyperplanes. Moreover, arrangements of finitely many tropical halfspaces can be…

In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.

We show that an optical system involving competing higher-order Kerr nonlinearities can support the existence of ultrasolitons, namely extremely localized modes that only appear above a certain threshold for the central intensity. Such new…

This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes -- convex polytopes -- through the addition of $N$ binary zonotope factors. The major contribution of…

We introduce combinatorial multivector fields, associate with them multivalued dynamics and study their topological features. Our combinatorial multivector fields generalize combinatorial vector fields of Forman. We define isolated…

We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…

Given an orientable surface with boundary and a free homotopy class, we present a purely combinatorial algorithm which produces a representative of that homotopy class with minimal self intersection.

We continue to study the holographic p-wave superconductor model in the Einstein-Maxwell-complex vector field theory with a non-minimal coupling between the complex vector field and the Maxwell field. In this paper we work in the AdS…

We review the relationship between discrete groups of symmetries of Euclidean three-space, constructions in algebraic geometry around Kleinian singularities including versions of Hilbert and Quot schemes, and their relationship to…

We explore several facets of tropical subrepresentations of a linear representation of a group over the tropical semifield $\mathbb{T}$. A key role in the study of tropical subrepresentations is played by two types of modules over a…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…

In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…

The paper deals with combinatorial and stochastic structures of cubical token systems. A cubical token system is an instance of a token system, which in turn is an instance of a transition system. It is shown that some basic results of…

A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…

This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations

Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…