Related papers: A Novel Approach To Particle Representations

Let $A$ be a ring with $1\neq 0$, not necessarily finite, endowed with an involution~$*$, that is, an anti-automorphism of order $\leq 2$. Let $H_n(A)$ be the additive group of all $n\times n$ hermitian matrices over $A$ relative to $*$.…

We extend a classification of irreducible, almost-commutative geometries whose spectral action is dynamically non-degenerate, to internal algebras that have six simple summands. We find essentially four particle models: An extension of the…

This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the…

This review paper contains a concise introduction to highest weight representations of infinite dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera…

We prove that particle models whose action is given by the integrated $n$-th curvature function over the world line possess $n+1$ gauge invariances. A geometrical characterization of these symmetries is obtained via Frenet equations by…

This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated…

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…

We determine all Lie groups compatible with the gauge structure of the Standard Elementary Particle Model (SM) and their representations. The groups are specified by congruence equations of quantum numbers. By comparison with the…

Let $R$ be a principal ideal local ring of finite length with a finite residue field of odd characteristic. Let $G(R)$ denote either the general linear group or the general unitary group of degree two over $R$. We study the decomposition of…

We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric,…

In this article, we study a weighted particle representation for a class of stochastic partial differential equations with Dirichlet boundary conditions. The locations and weights of the particles satisfy an infinite system of stochastic…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…

We classify the irreducible representations of a family of finite-dimensional pointed liftings $H_\lambda$ of the Nichols algebra associated with the diagram $A_2$ with parameter $q=-1$. We show that these algebras have infinite…

The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…

In this paper, we propose a simple yet effective method to represent point clouds as sets of samples drawn from a cloud-specific probability distribution. This interpretation matches intrinsic characteristics of point clouds: the number of…

We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constrains. The Krajewski diagrams…

In this article, we construct affine group schemes $GL(X)$ where $X$ is any object in the Verlinde category in characteristic $p$ and classify their irreducible representations. We begin by showing that for a simple object $X$ of…

We begin a study of the representation theory of quantum continuous $\mathfrak{gl}_\infty$, which we denote by $\mathcal E$. This algebra depends on two parameters and is a deformed version of the enveloping algebra of the Lie algebra of…

We classify finite-dimensional irreducible highest weight modules of generalized quantum groups whose positive part is infinite dimensional and has a Kharchenko's PBW basis with an irreducible finite positive root system.