Categories of Symmetries and Infinite-Dimensional Groups

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 This work contains the first explicit construction of hidden structures (mantles and trains). The author shows 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. 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 ...

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
This work contains the first explicit construction of hidden structures (mantles and trains). The author shows 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.

Inhalt
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

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