Related papers: A geometric interpretation and explicit form for h…
We define Hecke operators on vector valued modular forms transforming with the Weil representation associated to a discriminant form. We describe the properties of the corresponding algebra of Hecke operators and study the action on modular…
The problem of equivalency for linear differential operators of the first order is discussed.
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
A semi-infinite weighted Hankel matrix with entries defined in terms of basic hypergeometric series is explicitly diagonalized as an operator on $\ell^{2}(\mathbb{N}_{0})$. The approach uses the fact that the operator commutes with a…
Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
We develop a theory of tensor categories over a field endowed with abstract operators. Our notion of a "field with operators", coming from work of Moosa and Scanlon, includes the familiar cases of differential and difference fields,…
This study is an attempt at generalizing the class of partially hypoelliptic differential operators to a class of pseudodifferential operators, Symbol ideals are formed on the set of lineality and we discuss suitable topologies that allow…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
We give a survey of recent work on the construction of differential operators on various types of modular forms (mod p). We also discuss a framework for determining the effect of such operators on the mod p Galois representations attached…
We introduce and study a new class of higher order differential operators defined on $\mathbb{R}^{n}$, which are built with H\"{o}rmander vector fields, homogeneous w.r.t. a family of dilations (but not left invariant w.r.t. any structure…
We define the concept of higher order differential operators on a general noncommutative, nonassociative superalgebra A, and show that a vertex operator superalgebra has plenty of them, namely modes of vertex operators. A linear operator…
The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equivalence of three different definitions of higher order…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…
We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.
We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal $\hbar$-differential operators over a map. We study constructions and examples of such operators,…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.