Related papers: Symmetric Systems and their Applications to Root S…

We initiate the study of an algebra of symmetries for the 3D Dirac-Dunkl operator associated with the Weyl group of the exceptional root system $G_2$. For this symmetry algebra, we give both an abstract definition and an explicit…

Twisted generalized Weyl algebras (TGWAs) $A(R,\sigma,t)$ are defined over a base ring $R$ by parameters $\sigma$ and $t$, where $\sigma$ is an $n$-tuple of automorphisms, and $t$ is an $n$-tuple of elements in the center of $R$. We show…

A new class of representations of affine Weyl groups on rational functions are constructed, in order to formulate discrete dynamical systems associated with affine root systems. As an application, some examples of difference and…

Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $\Gamma < G$ an irreducible lattice. Consider the group measure space von Neumann algebra…

In this paper we discuss on the phenomenological viability of nonmetricity theories of gravity which are based in the class of generalized Weyl spacetimes -- denoted by $W_4$ -- where arbitrary nonmetricity is allowed. This class of…

In this paper, we study a family of generalized Weyl algebras $\{\A\}$ and their polynomial extensions. We will show that the algebra $\A$ has a simple localization $\A_{\mathbb{S}}$ when none of $p$ and $q$ is a root of unity. As an…

If $A$ is a unital associative ring and $\ell \geq 2$, then the general linear group $\mathrm{GL}(\ell, A)$ has root subgroups $U_\alpha$ and Weyl elements $n_\alpha$ for $\alpha$ from the root system of type $\mathsf A_{\ell - 1}$.…

Let W be an Iwahori-Weyl group of a connected reductive group G over a non-archimedean local field. I prove that if w is an element of W that does not act on the corresponding apartment of G by a translation then one can apply to w a…

This is the first of two papers on the superselection sectors of the conformal model in the title, in a time zero formulation. A classification of the sectors of the net of observables as restrictions of solitonic (twisted) and…

Let G be a semisimple algebraic group over an algebraically closed field of characteristic p>0, and let g be its Lie algebra. The crucial Lie algebra representations to understand are those associated with the reduced enveloping algebra…

We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure,…

We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic…

Let G be a group and let W be an algebra over a field K. We will say that W is a G-graded twisted algebra if W can be written as a direct sum over the elements of G of one dimensional K-vector spaces. It is also assumed that W has no…

Generalized Baxter's TQ-relations and the QQ-system are systems of algebraic relations in the category O of representations of the Borel subalgebra of the quantum affine algebra U_q(g^), which we established in our earlier works…

It is a well-known fact that every group $G$ has a presentation of the form $G = F/R$, where $F$ is a free group and $R$ the kernel of the natural epimorphism from $F$ onto $G$. Driven by the desire to obtain a similar presentation of the…

This paper introduces and systematically studies a class of Weyl-type algebras enriched with hyperbolic sine and power generators over a field of characteristic zero, defined as $A_{p,t,\cA} = \Weyl{\sinh(\pm x^{p} \sinh(t)),\; \sinh(\cA…

We propose an $n$-dimensional analogue of elliptic difference Painlev\'e equation. Some Weyl group acts on a family of rational varieties obtained by successive blow-ups at $m$ points in $\mpp^n(\mc)$, and in many cases they include the…

In the first part of the paper kernels are constructed which meromorphically extend the Macdonald-Koornwinder polynomials in their degrees. In the second part of the paper the kernels associated with rank one root systems are used to define…

The `Weyl symmetric functions' studied here naturally generalize classical symmetric (polynomial) functions, and `Weyl bialternants,' sometimes also called Weyl characters, analogize the Schur functions. For this generalization, the…

The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…