Vertex operator algebra theory is a new area of mathematics. It has been an exciting and
ever-growing subject from the beginning, starting even before R. Borcherds introduced the …

Vertex algebras are algebraic objects that encapsulate the concept of operator product
expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming …

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of
these quantum monodromy matrices, which will be called as “T-operators,” act in highest …

We construct a representation of the affine W-algebra of gl_r on the equivariant homology
space of the moduli space of U r-instantons, and we identify the corresponding module. As a …

The review is based on the authro's papers since 1985 in which a new approach to the
separation of variables (SoV) has being developed. It is argued that SoV, understood …

This paper is a direct continuation of 1 where we began the study of the integrable structures
in Conformal Field Theory. We show here how to construct the operators \bfQ_±(λ) which act …

In the paper [Dr3] V. Drinfeld formulated a number of problems in quantum group theory. In
particular, he raised the question about the existence of a quantization for Lie bialgebras …

In this paper we fill some gaps in the arguments of our previous papers [1, 2]. In particular,
we give a proof that the L operators of Conformal Field Theory indeed satisfy the defining …

Page 1 BORIS A. KHESIN ROBERT WENDT Volume 51 Ergebnisse der Mathematik und ihrer
Grenzgebiete 3. Folge A Series of Modern Surveys in Mathematics The Geometry of …

The Langlands Program has emerged in recent years as a blueprint for a Grand Unified
Theory of Mathematics. Conceived initially as a bridge between Number Theory and …