Symmetric Functions and Hall Polynomials / Edition 2

Symmetric Functions and Hall Polynomials / Edition 2

by I. G. MacDonald
     
 

ISBN-10: 0198504500

ISBN-13: 9780198504504

Pub. Date: 07/28/1999

Publisher: Oxford University Press, USA

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.

Overview

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.

Product Details

ISBN-13:
9780198504504
Publisher:
Oxford University Press, USA
Publication date:
07/28/1999
Series:
Oxford Mathematical Monographs Series
Edition description:
REV
Pages:
488
Product dimensions:
9.00(w) x 6.10(h) x 1.20(d)

Table of Contents

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. The LR-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 polynomials R*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's Q-functions
IV. The Characters of GL[n over a Finite Field
1. The groups L and M
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 of GL[n over a Local Field
1. Local fields
2. The Hecke ring H(G,K)
3. Spherical functions
4. Hecke series and zeta functions for GL[n(F)
5. Hecke series and zeta functions for GSp[2[n(F)
VI. Symmetric Functions with Two Parameters
1. Introduction
2. Orthogonality
3. The operators Dr/n
4. The symmetric functions P*l(x;q,t)
5. Duality
6. Pieri formulas
7. The skew functions P*l/µ, Q*l/µ
8. Integral forms
9. Another scalar product
10. Jack's symmetric functions
VII. Zonal Polynomials
1. Gelfand pairs and zonal spherical functions
2. The Gelfand pair (S[2[n, H[n)
3. The Gelfand pair (GL[n(R),O(n))
4. Integral formulas
5. The complex case
6. The quaternionic case
Bibliography
Notation
Index

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