Read more
Zusatztext Neretin's monograph is written in a colloquial style which sometimes reads more like the transcript of a good seminar, with numerous digressions and fascinating asides. His unconventional approach is apparent from the outset... the writing is clear. Klappentext There are many types of infinite-dimensional groups, most of which have been studied separately from each other since the 1950s. It is now possible to fit these apparently disparate groups into one coherent picture. With the first explicit construction of hidden structures (mantles and trains), Neretin is able to show how many infinite-dimensional groups are in fact only a small part of a much larger object, analogous to the way real numbers are embedded within complex numbers. Zusammenfassung For mathematicians working in group theory, the study of the many infinite-dimensional groups has been carried out in an individual and non-coherent way. For the first time, these apparently disparate groups have been placed together, in order to construct the `big picture'. This book successfully gives an account of this - and shows how such seemingly dissimilar types such as the various groups of operators on Hilbert spaces, or current groups are shown to belong to a bigger entitity. This is a ground-breaking text will be important reading for advanced undergraduate and graduate mathematicians. Inhaltsverzeichnis Preface 1: Visible and invisible structures on infinite-dimensional groups 2: Spinor representation 3: Representations of the complex classical categories 4: Fermion Fock space 5: The Weil representation: finite-dimensional case 6: The Weil representation: infinite-dimensional case 7: Representations of the diffeomorphisms of a circle and the Virasoro algebra 8: The heavy groups 9: Infinite-dimensional classical groups and almost invariant structures 10: Some algebraic constructions of measure theory Appendix A The real classical categories Appendix B Semple complexes, hinges, and boundaries of symmetric spaces Appendix C Boson-fermion correspondence Appendix D Univalent functions and the Grunsky operator Appendix E Characteristic Livsic function Appendix F Examples, counterexamples, notes References Index ...
