Related papers: Matrix valued commuting differential operators wit…
Let $G$ be the identity component of the isometry group for an arbitrary curved two-point homogeneous space $M$. We consider algebras of $G$-invariant differential operators on bundles of unit spheres over $M$. The generators of this…
Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with…
Denote by $SL_3(\mathbb R)$ the special linear group of degree 3 over the real numbers, $A$ the subgroup consisting of the diagonal matrices with positive entries. In this paper, we study the algebraic and analytic properties of the…
Let $G/K$ be a Hermitian symmetric space and $V_\tau$ an irreducible representation of $K$. We study the ring $\mathcal D^G(G/K, V_\tau)$ of $G$-invariant differential operators on sections of vector bundles $G\times_{(K, \tau)} V_\tau$…
We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.
In this paper we propose a very effective method for constructing matrix commuting differential operators of rank 2 and vector rank (2,2). We find new matrix commuting differential operators L, M of orders 2 and 2g respectively.
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
We present an orthogonal basis of gauge invariant operators constructed from some complex matrices for the free matrix field, where operators are expressed with the help of Brauer algebra. This is a generalisation of our previous work for a…
In this paper we study the properties of multiplication invariant (MI) operators acting on subspaces of the vector-valued space $L^2(X;\mathcal H)$. We characterize such operators in terms of range functions by showing that there is an…
We give two examples of algebras of differential operators associated to families of matrix valued orthogonal polynomials arising from representations of SU$(N+1)$. The first one gives a commutative algebra and the second one a…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitrary order attached to Gegenbauer polynomials.…
In this paper we study self-adjoint commuting ordinary differential operators with polynomial coefficients. These operators define commutative subalgebras of the first Weyl algebra. We find new examples of commuting operators of rank 2.
Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix…
We provide an explicit set of algebraically independent generators for the algebra of invariant differential operators on the Riemannian symmetric space associated with $\SL_n(\R)$.
In this paper we find coomon eigenfunctions of commuting differential operators of rank 2 with polynomial coefficients in some partial cases.
We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms…