Related papers: Matrix commuting differential operators of rank 2

Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…

We study intertwining relations for $n\times n$ matrix non-Hermitian, in general, one-dimensional Hamiltonians by $n\times n$ matrix linear differential operators with nondegenerate coefficients at $d/dx$ in the highest degree. Some methods…

The study of neutrinoless double beta decays of nuclei and hyperons require the calculation of hadronic matrix elements of local four-quark operators that change the total charge by two units \Delta Q=2 . Using a low energy effective…

Part I. We prove a one-to-one correspondence between differential symmetry breaking operators for equivariant vector bundles over two homogeneous spaces and certain homomorphisms for representations of two Lie algebras, in connection with…

Divided difference operators are degree-reducing operators on the cohomology of flag varieties that are used to compute algebraic invariants of the ring (for instance, structure constants). We identify divided difference operators on the…

We calculate the exchange relations of vertex operators of $U_q(\hat{sl_2})$ at level-two from its bosonic realization. The corresponding invertibility relation of type I vertex operators is also studied.

We calculate massive 5-propagator 2-loop integrals for operator matrix elements in the light-cone expansion, using Mellin-Barnes techniques and representations through generalized hypergeometric functions.

We construct and give a complete classification of all the differential symmetry breaking operators $\mathbb{D}_{\lambda, \nu}^{N,m}: C^\infty(S^3, \mathcal{V}_\lambda^{2N+1}) \rightarrow C^\infty(S^2, \mathcal{L}_{m, \nu})$, between the…

Relations between half- and full-lattice CMV operators with scalar- and matrix-valued Verblunsky coefficients are investigated. In particular, the decoupling of full-lattice CMV operators into a direct sum of two half-lattice CMV operators…

In this paper we study rank two commuting ordinary differential operators with polynomial coefficients and the orbit space of the automorphisms group of the first Weyl algebra on such operators. We prove that for arbitrary fixed spectral…

We construct and classify superconformally covariant differential operators defined on N=2 super Riemann surfaces. By contrast to the N=1 theory, these operators give rise to partial rather than ordinary differential equations which leads…

In the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant…

We derive the most general families of differential operators of first and second degree semi-commuting with the differential operators of the Heun class. Among these families we classify all those families commuting with the Heun class. In…

In this work we classify all the order-two Hypergeometric operators $D$, symmetric with respect to some $2\times 2$ irreducible matrix-weight $W$ such that $DP_n=P_n\left(\begin{smallmatrix} \lambda_n&0\\0&\mu_n \end{smallmatrix} \right)$…

The spectral decomposition for an explicit second-order differential operator $T$ is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with…

We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct…

We review the quadratic form of the Laplace operator in 3 dimensions in spehrical coordinates which acts on the transverse components of vector functions. Operators, acting on the parametrizing functions of one of the transverse components…

Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factorable symbol. It is proved that ``irreducible'' parametric…

We study the variety of n by n matrices with commutator of rank at most one. We describe its irreducible components; two of them correspond to the pairs of commuting matrices, and n-2 components of smaller dimension corresponding to the…

We consider first order linear operators commuting with the operator appearing in the linearized equation of motion of Rarita-Schwinger fields which comes directly from the action. First we consider a simplified operator giving an equation…