Related papers: Contact superconformal algebras and their represen…
In this work we construct an embedding of a nontrivial central extension of the contact superconformal algebra K'(4) into the Lie superalgebra of pseudodifferential symbols on the supercircle S^{1|2}. Associated with this embedding is a…
Let K be the Lie superalgebra of contact vector fields on the supersymmetric line. We compute the action of K on the modules of differential and pseudodifferential operators between spaces of tensor densities, in terms of their conformal…
We give a general construction of realizations of the contact superconformal algebras $K(2)$ and $\hat{K}'(4)$, and the exceptional superconformal algebra $CK_6$ as subsuperalgebras of matrices over a Weyl algebra of size $2^N\times 2^N$,…
The superalgebra $\hat{K}'(4)$ and the exceptional N = 6 superconformal algebra have ``small'' irreducible representations in the superspaces $V^{\mu} = t^{\mu}\C[t, t^{-1}]\otimes\Lambda(N)$, where N = 2 and 3, respectively. For ${\mu \in…
A class of Fock representations of non-central extensions of the super-diffeomorphism algebra in (N+1|M) dimensions is constructed, by superization of the paper [physics/9705040]. The representations act on trajectories in (N|M)-dimensional…
We classify nontrivial deformations of the standard embedding of the Lie superalgebra K(1) of contact vector fields on the (1,1)-dimensional supercircle into the Lie superalgebra of superpseudodifferential operators on the supercircle. This…
We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\"obius superalgebra $osp(1|2)$. We…
We realize the exceptional superconformal algebra $CK_6$, spanned by 32 fields, inside the Lie superalgebra of pseudodifferential symbols on the supercircle $S^{1|3}$. We obtain a one-parameter family of irreducible representations of…
We investigate the first cohomology space associated with the embedding of the Lie superalgebra $\cK(2)$ of contact vector fields on the (1,2)-dimensional supercircle $S^{1\mid 2}$ in the Lie superalgebra $\cS\Psi \cD \cO(S^{1\mid 2})$ of…
We study non-trivial deformations of the natural action of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ of th espace of symbols. We calculate obstructions for integrability…
We study the superconformally covariant pseudodifferential symbols defined on N=2 super Riemann surfaces. This allows us to construct a primary basis for N=2 super W_KP^(n)-algebras and, by reduction, for N=2 super W_n-algebras.
We obtain an embedding of a one-parameter family of exceptional simple Lie superalgebras $D(2, 1 ; \alpha)$ into the Lie superalgebra of pseudodifferential symbols on the supercircle $S^{1|2}$. Correspondingly, there is an embedding of…
Following Feigin and Fuchs, we compute the first cohomology of the Lie superalgebra $\mathcal{K}(1)$ of contact vector fields on the (1,1)-dimensional real superspace with coefficients in the superspace of linear differential operators…
In the last six years remarkable developments have taken place concerning the representation theory of N=2 superconformal algebras. Here we present the highlights of such developments.
The algebraic structure on the subspace of the quasi-primary vectors given by the projection of the (n) products of a conformal superalgebra is formulated. As an application the complete list of simple physical conformal superalgebras is…
We discuss the appearance of Jacobi automorphic forms in the theory of superconformal vertex algebras, explaining it by way of supercurves and formal geometry. We touch on related topics such as Ramanujan's differential equations for…
We give an introduction to conformal and superconformal algebras and their representations in various dimensions. Special emphasis is put on 4d $\mathcal{N}=2$ superconformal symmetry. This is the writeup of the lectures given at the Winter…
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…
We reexamine the relation between contact structures on supermanifolds and supersymmetric mechanics in the superspace formulation. This allows one to use the language of contact geometry when dealing with the d = 1, N = 2 super-Poincare…
We observe a correspondence between the zero modes of superconformal algebras $S'(2, 1)$ and W(4) and the Lie superalgebras formed by classical operators appearing in the K{\"a}hler and hyper-K{\"a}hler geometry.