Categories of Symmetries and Infinite-Dimensional Groups

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.

• 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