Symmetric Functions and Hall Polynomials [Paperback]

This new and much expanded edition of a well-received book remains the only text available on the subject of symmetric functions and Hall polynomials. There are new sections in almost every chapter, and many new examples have been included throughout.

I. Symmetric Functions
1. Partitions
2. The ring of symmetric functions
3. Schur functions
4. Orthogonality
5. Skew Schur functions
6. Transition matrices
7. The characters of the symmetric groups
8. Plethysm
9. The Littlewood-Richardson rule
Appendix A: Polynomial functors and polynomial representations
Appendix B: Characters of wreath products
II. Hall Polynomials
1. Finite o-modules
2. The Hall algebra
3. TheLR-sequence of a submodule
4. The Hall polynomial
Appendix (by A. Zelevinsky): Another proof of Hall's theorem
III. Hall-Littlewood Symmetric Functions
1. The symmetric polynomialsR*l
2. Hall-Littlewood functions
3. The Hall algebra again
4. Orthogonality
5. Skew Hall-Littlewood functions
6. Transition matrices
7. Green's polynomials
8. Schur'sQ-functions
IV. The Characters ofGL[nover a Finite Field
1. The groupsLandM
2. Conjugacy classes
3. Induction from parabolic subgroups
4. The characteristic map
5. Construction of the characters
6. The irreducible characters
Appendix: proof of (5.1)
V. The Hecke Ring ofGL[nover a Local Field
1. Local fields
2. The Hecke ringH(G,K)
3. Spherical functions
4. Hecke series and zeta functions forGL[n(F)
5. Hecke series and zeta functions forGSp[2[n(F)
VI. Symmetric Functions with Two Parameters
1. Introduction
2. Orthogonality
3. The operatorsDr/n
4. The symmetric functionslé