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.

• 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