Categories of Symmetries and Infinite-Dimensional Groups

by Yu A. Neretin, G. G. Gould

Overview

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.

Product Details

ISBN-13:	9780198511861
Publisher:	Oxford University Press
Publication date:	09/12/1996
Series:	London Mathematical Society Monographs , #16
Pages:	432
Product dimensions:	6.38(w) x 9.50(h) x 1.14(d)

About the Author

Institute of Electronic Machine Building, Moscow

Table of Contents

Preface1. Visible and invisible structures on infinite-dimensional groups2. Spinor representation3. Representations of the complex classical categories4. Fermion Fock space5. The Weil representation: finite-dimensional case6. The Weil representation: infinite-dimensional case7. Representations of the diffeomorphisms of a circle and the Virasoro algebra8. The heavy groups9. Infinite-dimensional classical groups and almost invariant structures10. Some algebraic constructions of measure theoryAppendix A The real classical categoriesAppendix B Semple complexes, hinges, and boundaries of symmetric spacesAppendix C Boson-fermion correspondenceAppendix D Univalent functions and the Grunsky operatorAppendix E Characteristic Livsic functionAppendix F Examples, counterexamples, notesReferencesIndex