Bombay lectures on highest weight representations of infinite dimensional Lie algebras (Q2865769)

This is the second edition of the classical book [\textit{V. G. Kac} and \textit{A. K. Raina}, Bombay lectures on highest weight representations of infinite dimensional Lie algebras. Singapore-New Jersey-Hong Kong: World Scientific (1987; Zbl 0668.17012)]. The present edition consists of two parts. The first part, Lectures~1--12, contains the largely unchanged text of the first edition. The second part, Lectures~13--18, is an extended write-up of a series of lectures on vertex operator algebras given by the first author at the Tata Institute of Fundamental Research at Mumbai (Bombay) in January 2003. The basic idea of the latter lectures was to show how the key notions of the theory of vertex algebras simplify and clarify the constructions from the first edition of this book.NEWLINENEWLINEIn more details, the second half of the book addresses, among others, the following subjects related to the theory of vertex algebras: formal distributions, formal Fourier transform, \(\lambda\)-bracket, restricted representations, twisted representations, quantum fields, normal order product, energy-momentum fields, conformal weights, non-commutative Wick formula, charge decomposition, Borcherds identity, Sugawara construction.NEWLINENEWLINEThe book contains many examples and several applications, in particular, to the Jacobi triple product identity.