Symmetric Functions and Hall Polynomials / Edition 2

by I. G. Macdonald

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
Publication date:	07/29/1999
Series:	Oxford Mathematical Monographs
Edition description:	REV
Pages:	488
Product dimensions:	9.04(w) x 6.32(h) x 0.95(d)

About the Author

I. G. Macdonald, Queen Mary and Westfield College, London

I. G. Macdonald, Emeritus Professor, Queen Mary and Westfield College, London

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/ , Q*l/
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

Editorial Reviews

"This new edition incorporates the additions to the translated version, as well as a tremendous amount of new material . . . . Readers familiar with the first edition will find that the author's uniquely brief but lucid style has not changed . . . . This masterful new edition will undoubtedly remain the standard reference for symmetric polynomials. It serves as proof of the metatheorem that wherever 'natural' structures indexed by partitions arise, the algebra of symmetric functions is nearby."—Mathematical Reviews

From the Publisher