Related papers: The generalized Casimir operator and tensor repres…

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…

Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was…

In rainbow tensor models, which generalize rectangular complex matrix model (RCM) and possess a huge gauge symmetry $U(N_1)\times\ldots\times U(N_r)$, we introduce a new sub-basis in the linear space of gauge invariant operators, which is a…

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For…

We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…

In this work we develop a general procedure for constructing the recursion operators fro non-linear integrable equations admitting Lax representation. Svereal new examples are given. In particular we find the recursion operators for some…

Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations;…

The generalized vector is defined on an $n$ dimensional manifold. Interior product, Lie derivative acting on generalized $p$-forms, $-1\le p\le n$ are introduced. Generalized commutator of two generalized vectors are defined. Adding a…

We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge…

Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of…

Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…

In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…

In recent years, algebras and modules of differential operators have been extensively studied. Equivariant quantization and dequantization establish a tight link between invariant operators connecting modules of differential operators on…

We prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the…

Using a derivative decomposition of the Hochschild differential complex we define a generalized inverse of the Hochschild coboundary operator. It can be applied for systematic computations of star products on Poisson manifolds.

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…

Proceeding in analogy with su(n) work on lambda matrices and f- and d-tensors, this paper develops the technology of the Lie algebra g2, its seven dimensional defining representation gamma and the full set of invariant tensors that arise in…

Any free nilpotent Lie algebra is determined by its rank and step. We consider free nilpotent Lie algebras of steps 3, 4 and corresponding connected and simply connected Lie groups. We construct Casimir functions of such groups, i.e.,…