Related papers: Algebraically special solutions in higher dimensio…
Let G be a simple reductive group over the complex numbers. Let W be the Weyl group of G. We propose a description of the Springer representations of W associated to various unipotent classes of G by a purely algebraic method involving the…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
We study the algebra of Weyl modules in types $A$ and $C$ using the methods of arcs over toric degenerations and functional realization of dual space. We compute the generators and relations of this algebra and construct its basis.
The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl…
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as…
Algebraic classification of higher dimensional, shear-free, twist-free, expanding (or non-expanding) spacetime is studied with the limit of $D\rightarrow\infty$. Similar to classification of any arbitrary dimension $D>4$, this spacetime is…
In this note a characterization of anallytically Riesz operators is given. This work completes the article [1].
In the paper, the authors establish some interesting identities and inequalities involving the extended Weyl type fractional integrals.
The solvability for infinite dimensional differential algebraic equations possessing a resolvent index and a Weierstra{\ss} form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which…
This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…
We solve a special type of linear systems with coefficients in multivariate polynomial rings. These systems arise in the computation of parametric Bernstein-Sato polynomials associated with certain hypergeometric ideals in the Weyl algebra.
In this paper we define the so-called twisted Heisenberg superalgebras over the complex number field by adding derivations to Heisenberg superalgebras. We classify the fine gradings up to equivalence on twisted Heisenberg superalgebras and…
We show that to determine all solvable elements in the Weyl algebra is closely related to the Dixmier's open question. Sufficient conditions for an elements being unsolvable are given, and properties of solvable elements are obtained.
We present new infinite-dimensional spaces of bi-axially symmetric asymptotically anti-de Sitter solutions to four-dimensional Vasiliev higher spin gravity, obtained by modifications of the Ansatz used in arXiv:1107.1217, which gave rise to…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
We investigate weight modules for finite and infinite Weyl algebras, classifying all such simple modules. We also study the representation type of the blocks of locally-finite weight module categories and describe indecomposable modules in…
Let W be a Weyl group. We define a class of irreducible representations of W that we call antispecial. They are in bijection with the constructible representations of W. We define an oriented graph structure on the set of antispecial…
Classical $W$-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension.…
We use decoupling theory to estimate the number of solutions for quadratic and cubic Parsell--Vinogradov systems in two dimensions.