Related papers: Riemann Surfaces and Vertex Operator Algebras

A covariant pseudodifferential calculus on Riemann surfaces, based on the Krichever-Novikov global picture, is presented. It allows defining scalar and matrix KP operators, together with their reductions, in higher genus. Globally defined…

We show that the secondary Hochschild cohomology associated to a triple $(A,B,\varepsilon)$ has several of the properties of the usual Hochschild cohomology. Among others, we prove the existence of the cup and Lie products, discuss the…

This paper is concerned with the primitive cohomology of a smooth projective hypersurface considered as a linear representation for its automorphism group. Using the Lefschetz-Riemann-Roch formula, the character of this representation is…

For a von Neumann algebra M on a Hilbert space, A. Connes has constructed a module S and a derivation of M into S, such that M is approximately finite dimensional if and only if that derivation is inner. The paper contains a generalization…

We characterize operators $T=PQ$ ($P,Q$ orthogonal projections in a Hilbert space $H$) which have a singular value decomposition. A spatial characterizations is given: this condition occurs if and only if there exist orthonormal bases…

We study analytic descriptions of conformal immersions of the Riemann sphere S^2 into the CP^(N-1) sigma model. In particular, an explicit expression for two-dimensional (2-D) surfaces, obtained from the generalized Weierstrass formula, is…

We construct geometrically the generating fields of a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes of n points on a projective surface for all n. We compute explicitly the commutators…

We discuss the reflexivity of hyperexpansions and their Cauchy dual operators. In particular, we show that any cyclic completely hyperexpansive operator is reflexive. We also establish the reflexivity of the Cauchy dual of an arbitrary…

Local Hochschild, cyclic Homology and K-theory were introduced by N. Teleman in [10] with the purpose of unifying different settings of the index theorem. This paper is one of the research topics announced in [10], {\S}10. The definition of…

We consider differential operators $L$ acting on functions on a Riemannian surface, $\Sigma$, of the form $$L = \Delta + V -a K ,$$where $\Delta$ is the Laplacian of $\Sigma$, $K$ is the Gaussian curvature, $a$ is a positive constant and $V…

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…

It is shown that any simple, rational and C_2-cofinite vertex operator algebra whose weight 1 subspace is zero, the dimension of weight 2 subspace is greater than or equal to 2 and with central charge c=1, is isomorphic to L(1/2,0)\otimes…

Let $m\in N$, $P(t)\in C[t]$. Then we have the Riemann surfaces (commutative algebras) $R_m(P)=C[t^{\pm1},u | u^m=P(t)]$ and $S_m(P)=C[t , u| u^m=P(t)].$ The Lie algebras $\mathcal{R}_m(P)=Der(R_m(P))$ and $\mathcal{S}_m(P)=Der(S_m(P))$ are…

We discuss the spectral decomposition of the hypergeometric differential operators on the line $\mathrm{Re}\, z=1/2$. Such operators arise in the problem of decomposition of tensor products of unitary representations of the universal…

For a linear nonvariational operator structured on smooth H\"ormander's vector fields, with H\"older continuous coefficients, we prove a regularity result in the spaces of H\"older functions. We deduce an analogous regularity result for…

We show that every ring isomorphism between the algebras of locally measurable operators for type II$_\infty$ von Neumann algebras is similar to a real $^*$-isomorphism. This together with previous results by the author and…

This note presents an analysis of a class of operator algebras constructed as cross-sectional algebras of flat holomorphic matrix bundles over a finitely bordered Riemann surface. These algebras are partly inspired by the bundle shifts of…

We consider Picard surfaces, locally symmetric varieties $S_{\Gamma}$ attached to the Lie group SU(2,1), and we construct explicit differential forms on $S_{\Gamma}$ representing Eisenstein classes, i.e. cohomology classes restricting…

The symmetry algebra $P_\infty = W_\infty \oplus H \oplus I_\infty$ of integrable systems is defined. As an example the classical Sophus Lie point symmetries of all higher KP equations are obtained. It is shown that one (``positive'') half…

Unifying various generalizations of the important notions of Reynolds operators, the relative cocycle weighted Reynolds operators are studied. Here cocycle weighted means the weight of the operators is given by a 2-cocycle rather than by a…