Symmetric Functions and Hall Polynomials
Series: Oxford Mathematical Monographs;
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Product details:
- Edition number 2
- Publisher Clarendon Press
- Date of Publication 9 July 1998
- ISBN 9780198504504
- Binding Paperback
- No. of pages488 pages
- Size 233x157x27 mm
- Weight 707 g
- Language English
- Illustrations line figures 0
Categories
Short description:
The only book available on the subject, this is a new and expanded edition of a widely acclaimed monograph. Almost every chapter has new sections and many new examples have been included throughout. New chapters on a family of symmetric functions rationally on two parameters, and on zonal polynomials bring this book up-to-date with research being conducted in the field
MoreLong description:
This is a new and much expanded edition of Professor Macdonald's acclaimed monograph on Symmetric Functions and Hall Polynomials. Almost every chapter has new sections and many new examples have been included throughout. In addition there are two new chapters (6 and 7).
Chapter 6 contains an extended account of a family of symmetric functions depending on two parameters. These symmetric functions include as particular cases many of those encountered earlier in the book and they also include, as a limiting case, Jack's symmetric functions depending on a parameter ?. Many of the properties of the Schur functions generalize to these two-parameter symmetric functions.
Chapter 7 is devoted to the study of the zxonal polynomials, long familiar to staticians. From one point of view, they are a special case of Jack's symmetric functions (the parameter ? being equal to 2) but their combinatorial and group-theoretic connections make them worthy of study in their own right.
Evidently this second edition will be the source and reference book for symmetric functions in the next future.
Table of Contents:
Symmetric Functions
Hall Polynomials
Hall-Littlewood symmetric functions
The Characters of GL[xn over a finite field
The Hecke ring of GL[xn over a local field
Symmetric functions with two parameters
Zonal polynomials
Notation
Bibliography
Index