Related papers: On a group-theoretical approach to the curl operat…
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 demonstrate that the matrix quantum group $SL_q(2)$ gives rise to nontrivial matrix product operator representations of the Lie group $SL(2)$, providing an explicit characterization of the nontrivial global $SU(2)$ symmetry of the XXZ…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
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…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.…
We construct a differential operator on sheaves of $p$-adic modular forms defined over the locus of $p$-rank $\ge 1$ of the Siegel threefold, by applying a revisited version of the approach that Sean Howe recently introduced in his paper "A…
Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…
A method of generating differential operators is used to solve the spectral problem for a generalisation of the Sylvester-Kac matrix. As a by-product, we find a linear differential operator with polynomial coefficients of the first order…
We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.
We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$. For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
In this paper, we present a functorial method to define ramification groups, identifying them as inertia groups of an induced action on composite jet algebras. This framework lays the foundation for defining higher ramification groups for…
We introduce a new perturbation for the operator curl related to connections with nonabelian gauge groups. We also prove that the perturbed operator is unitary equivalent to the operator curl if the corresponding connection is close enough…
We present algorithms for the group independent reduction of group theory factors of Feynman diagrams. We also give formulas and values for a large number of group invariants in which the group theory factors are expressed. This includes…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In…
Quantum Teichmuller theory assigns invariants to three-manifolds via projective representations of mapping class groups derived from the representation of a noncommutative torus. Here, we focus on a representation of the simplest…
We characterize some variations of pseudoskeleton (also called CUR) decompositions for matrices and tensors over arbitrary fields. These characterizations extend previous results to arbitrary fields and to decompositions which use…
With techniques borrowed from quantum information theory, we develop a method to systematically obtain operator inequalities and identities in several matrix variables. These take the form of trace polynomials: polynomial-like expressions…