This book gives a complete and self-contained account of what is known about the subject and is written from a geometrical and analytical point of view, with quantum field theory very much in mind.
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'This is an outstanding book, of enormous interest to anyone interested in Lie groups, Lie algebras and/or Quantum Field Theory' Mathematika
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Introduction; PART 1 - Finite dimensional lie groups; Groups of smooth maps; Central extensions; The root system: KAC-Moody algebras; Loop groups as groups of operators in Hilbert space; The Grassmannian of Hilbert space and the determinant line bundle; The fundamental homogeneous space. PART 2 - Representation theory; The fundamental representation; The Borel-Weil theory; The spin representation; 'Blips' or 'vertex operators'; The KAC character formula and the
Bernstein-Gelfand-Gelfand resolution; References; Index of notation; Index.