This paper is devoted to recent progress made towards the understanding of closed bosonic
and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean …

This paper gives the mathematical foundations for the BRS quantization procedure. We first
discuss the classical finite dimensional BRS procedure and relate it to Marsden-Weinstein …

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 …

0.1. Let X be a connected smooth projective curve over C of genus g> 1, G a semisimple
group over C, g the Lie algebra of G. Denote by BunG= BunG (X) the moduli stack of G …

The first edition of this book is a collection of a series of lectures given by Professor Victor
Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus …

We show that the quantum Drinfeld-Sokolov reduction of the affine Kac-Moody algebra sl (n)
Λ gives the Wn-algebra of Fateev-Zamolodchikov-Lukyanov. We derive this Wn-algebra …

This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in
Dec'85 and Jan'86. These lectures focus on the idea of a highest weight representation …

We study representations of affine Kac-Moody algebras from a geometric point of view. It is
shown that Wakimoto modules introduced in [18], which are important in conformal field …

We prove the long-standing conjecture on the coset construction of the minimal series
principal W-algebras of ADE types in full generality. We do this by first establishing Feigin's …