Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 1 Examples
- 2 KP flows and the Sato–Segal–Wilson Grassmannian
- 3 The KP hierarchy and its standard reductions
- 4 Infinite dimensional Grassmannians
- 5 Fermionic representation of τ-functions and Baker functions
- 6 Finite dimensional reductions of the infinite Grassmannian and their associated τ-functions
- 7 Other related integrable hierarchies
- 8 Convolution symmetries
- 9 Isomonodromic deformations
- 10 Integrable integral operators and dual isomonodromicdeformations
- 11 Random matrix models I. Partitions functions and correlators
- 12 Random matrix models II. Level spacings
- 13 Generating functions for characters, intersection indicesand Brézin–Hikami matrix models
- 14 Generating functions for weighted Hurwitz numbers:enumeration of branched coverings
- Appendix A Integer partitions
- Appendix B Determinantal and Pfaffian identities
- Appendix C Grassmann manifolds and flag manifolds
- Appendix D Symmetric functions
- Appendix E Finite dimensional fermions:Clifford and Grassmann algebras,spinors, isotropic Grassmannians
- Appendix F Riemann surfaces, holomorphic differentialsand θ functions
- Appendix G Orthogonal polynomials
- Appendix H Solutions of selected exercises
- References
- List of Symbols
- Index
Frontmatter
Published online by Cambridge University Press: 21 January 2021
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 1 Examples
- 2 KP flows and the Sato–Segal–Wilson Grassmannian
- 3 The KP hierarchy and its standard reductions
- 4 Infinite dimensional Grassmannians
- 5 Fermionic representation of τ-functions and Baker functions
- 6 Finite dimensional reductions of the infinite Grassmannian and their associated τ-functions
- 7 Other related integrable hierarchies
- 8 Convolution symmetries
- 9 Isomonodromic deformations
- 10 Integrable integral operators and dual isomonodromicdeformations
- 11 Random matrix models I. Partitions functions and correlators
- 12 Random matrix models II. Level spacings
- 13 Generating functions for characters, intersection indicesand Brézin–Hikami matrix models
- 14 Generating functions for weighted Hurwitz numbers:enumeration of branched coverings
- Appendix A Integer partitions
- Appendix B Determinantal and Pfaffian identities
- Appendix C Grassmann manifolds and flag manifolds
- Appendix D Symmetric functions
- Appendix E Finite dimensional fermions:Clifford and Grassmann algebras,spinors, isotropic Grassmannians
- Appendix F Riemann surfaces, holomorphic differentialsand θ functions
- Appendix G Orthogonal polynomials
- Appendix H Solutions of selected exercises
- References
- List of Symbols
- Index
Summary
![Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'](https://static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Abook%3A9781108610902/resource/name/firstPage-9781108492683pre_i-vi.jpg)
- Type
- Chapter
- Information
- Tau Functions and their Applications , pp. i - viPublisher: Cambridge University PressPrint publication year: 2021