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
13 - Generating functions for characters, intersection indicesand Brézin–Hikami matrix models
Published online by Cambridge University Press: 21 January 2021
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
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- Tau Functions and their Applications , pp. 356 - 368Publisher: Cambridge University PressPrint publication year: 2021