Bounded Littlewood Identities.

Cover
Title page
Acknowledgements
Chapter 1. Introduction
1.1. Littlewood identities
1.2. Outline
Chapter 2. Macdonald-Koornwinder theory
2.1. Partitions
2.2. Generalised -shifted factorials
2.3. Rogers-Szegő polynomials
2.4. Plethystic notation
2.5. Macdonald polynomials
2.6. Koornwinder polynomials
2.7. Macdonald-Koornwinder polynomials
2.8. Hall-Littlewood polynomials
Chapter 3. Virtual Koornwinder integrals
3.1. Basic definitions
3.2. Closed-form evaluations-the Macdonald case
3.3. Closed-form evaluations-the Hall-Littlewood case
Chapter 4. Bounded Littlewood identities
4.1. Statement of results
4.2. Proofs of Theorems 4.1-4.8
Chapter 5. Applications
5.1. Plane partitions
5.2. Character identities for affine Lie algebras
5.3. Rogers-Ramanujan identities
5.4. Quadratic transformations for Kaneko-Macdonald-type basic hypergeometric series
Chapter 6. Open problems
6.1. Missing -analogues
6.2. Littlewood identities for near-rectangular partitions
6.3. Littlewood identities of Pfaffian type
6.4. Elliptic Littlewood identities
6.5. , -Littlewood-Richardson coefficients
6.6. Dyson-Macdonald-type identities
Appendix A. The Weyl-Kac formula
Appendix B. Limits of elliptic hypergeometric integrals
Bibliography
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