Related papers: Vertex algebras and elliptic genera
Research Briefs: Does the GSL imply an entropy bound?, by Warren G. Anderson A lightweight review of middleweight black holes, by Ben Bromley The physics of isolated horizons, by Daniel Sudarsky LIGO project update, by Stan Whitcomb Meeting…
We give a coset realization of the vertex operator algebra $M(1)^+$ with central charge $\ell$. We realize $M(1)^+$ as a commutant of certain affine vertex algebras of level -1 in the vertex algebra $L_{C_{\ell}…
An outline is sketched, of applications of the ideas and the mathematical methods presented at the 19th symposium of the Hellenic Nuclear Physics Society (HNPS) in Thessaloniki, May 2010
The aim of this text is to provide an elementary and self-contained exposition of Gromov's argument on topological overlap (the presentation is based on Gromov's work, as well as two follow-up papers of Matousek and Wagner, and of…
In this work we give an explicit solution to the problem of differentiation of hyperelliptic functions in genus $4$ case. It is a genus $4$ analogue of the classical result of F. G. Frobenius and L. Stickelberger [F. G. Frobenius, L.…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
A Comment on the Letter by Raphael Blumenfeld and Sam F. Edwards, [Phys. Rev. Lett. 90, 114303 (2003)].
We prove some combinatorial conjectures extending those proposed in [13, 14]. The proof uses a vertex operator due to Nekrasov, Okounkov, and the first author [4] to obtain a "gluing formula" for the relevant generating series, essentially…
This is an expository paper on rationally connected varieties. The aim is to provide an introduction to the subject, as well as to discuss a recent result by T. Graber, J. Harris and J. Starr. The paper is based on the talk I gave at the…
I show that the new topological field theories recently associated by Dubrovin with each Coxeter group may be all obtained in a simple way by a ``restriction'' of the standard ADE solutions. I then study the Chebichev specializations of…
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…
This paper surveys results on the connections between the cohomology for algebraic groups, finite groups and Frobenius kernels that were presented at the Workshop and Summer School on Lie and Representation Theory at East China Normal…
In the paper, developing the idea of V. Sokolov et all. (J.Math.Phys. 40 (1999)6473 we construct recursion operators and hereditary algebra of symmetries for many field and lattice systems.
This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.
This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove…
Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we investigate the vertex operators of the elliptic quantum group U_{q,p}(\widedhat{sl}_2) defined as intertwining operators of infinite dimensional…
Using methods from algebraic topology and group cohomology, I pursue Grothendieck's question on equality of geometric and cohomological Brauer groups in the context of complex-analytic spaces. The main result is that equality holds under…
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
Borisov and Libgober recently proved a conjecture of Dijkgraaf, Moore, Verlinde, and Verlinde on the elliptic genus of a Hilbert scheme of points on a surface. We show how their result can be used together with our work on complex genera of…
The research monograph gives the first systematic exposition of the elliptic (scalar and matrix) operators theory and elliptic boundary-value problems in the scales of Hilbert spaces of H\"ormander of the functions/distributions of…