Related papers: Classification of differential symmetry breaking o…
We consider linear spectral-meromorphic (s-meromorphic) OD operators at the real axis such that all local solutions to the eigenvalue problems are meromorphic for all $\lambda$. By definition, rank one algebro-geometrical operator $L$ admit…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
We classify anti-involutions of Lie superalgebra $\hsd$ preserving the principal gradation, where $\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations…
Let $D:\Omega\xrightarrow{}\Omega$ be a differential operator defined in the exterior algebra $\Omega$ of differential forms over the polynomial ring $S$ in $n$ variables. In this work we give conditions for deforming the module structure…
Based on the Lie theoretical methods of algebraic Fourier transformation, we classify in the case of generic values of inducing parameters the scalar singular vectors corresponding to the diagonal branching rules for scalar generalized…
We prove that the scalar and $2\times 2$ matrix differential operators which preserve the simplest scalar and vector-valued polynomial modules in two variables have a fundamental Lie algebraic structure. Our approach is based on a general…
We introduce the notion of Hitchin variety over $\C$. Let $L$ be a holomorphic line bundle over a Hitchin variety $X$. We investigate the space of all global sections of sheaf of differential operators $\cat{D}^k (L)$ and symmetric powers…
In this paper we investigate the spectrum of the differential operators generated by the ordinary differential expression of odd order with PT-symmertic periodic matrix coefficients
We give a complete classification of tangential bidifferential operators of total order at most $n$ which are expressed purely in terms of the Laplacian on the ambient space of an $n$-dimensional manifold. This gives a curved analogue of…
Several definitions of differential operators on modules over noncommutative rings are discussed.
This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior…
The isomorphism between the reduction algebra and the invariant differential operators on G/H is sketched.
In the present paper we review our project of systematic construction of invariant differential operators on the example of the non-compact algebras su(n,n) for n=2,3,4. We give explicitly the main multiplets of indecomposable elementary…
We provide detailed holomorphic Morse estimates for the cohomology of sheaves of jet differentials and their dual sheaves. These estimates apply on arbitrary directed varieties, and a special attention has been given to the analysis of the…
Based on an original classification of differential equations by types of regular Lie group actions, we offer a systematic procedure for describing partial differential equations with prescribed symmetry groups. Using a new powerful…
We propose a definition of differential operators of an associative algebra $A$ in the spirit of Hochschild cohomology. Specifically we define $D(A)$ as the zero cohomology of a certain bicomplex formed by Hom-spaces…
Let $V$ be a vector space over a field $\mathbb F$ with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If $\mathbb F=\mathbb C$, then we give canonical matrices of isometric and selfadjoint…
We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
We consider generalized Hodge-Laplace operators $\alpha d \delta + \beta \delta d$ for $\alpha, \beta > 0$ on $p$-forms on compact Riemannian manifolds. In the case of flat tori and round spheres of different radii, we explicitly calculate…