Infinite-Dimensional Lie Algebras

Abstract

This is the third, substantially revised edition of this important monograph. The book is concerned with Kac–Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.

An Approach to Script N = 4 ADE Gauge Theory onK3

“…The second one is that 1/η(τ /N ) can be written as the form θ 2 A N−1 (τ )/η(τ ) N , where θ 2 A N−1 (τ ) is a kind of A N −1 theta function [7]. This identity is easily verified from the celebrated denominator identity of the affine Lie algebra [8,12]. These two facts enabled us to rewrite the partition function of SU (N ) theory on K3 into the desired form.…”

Free fermion resolution of supergroup WZNW models

“…Relation (5.4) may also be extended to a statement about non-specialized characters since the fermions p a and θ a are charged under the bosonic generators K i . If g 0 is a simple Lie algebra the characters of the unitarŷ g ren 0 -modules V µ can be looked up in [61,62]. They form a finite dimensional unitary representation of the modular group.…”

Macdonald’s constant term conjectures for exceptional root systems

“…Since every affine root system is a direct sum of irreducible ones [Mai,Kac,Hu2], it suffices to prove the conjecture for the latter. Recently, Gustafson [Gu] completed the proof of Macdonald's conjecture for all the infinite families by proving it for the infinite families S (C n …”