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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Fler böcker av Andrew Pressley
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<br>"The authors have done an important service in giving the first coherent account of the geometric representation theory and structure of loop groups and their central extensions....Besides mathematicians working on infinite-dimensional groups and manifolds, the book is to be recommended for theoretical physicists working in quantum field theory, completely integrable systems and string theory." --Mathematical Reviews<br>"This book is the first account, from a mathematical point of view, of what is known about the global analysis of loop groups--a particular kind of infinite dimensional group consisting of maps from a circle to a fixed (finite dimensional) group. These objects arise naturally in one dimensional field theories and 'string' models. Loop Groups is remarkably comprehensive and coherent. . . . Although many of the results are at the cutting edge of research, the exposition and proofs are elegant and intelligible. The future influence of the book may be hard to overstate.
Bloggat om Loop Groups
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.