
Noncommutative Character Theory Of The Symmetric Group
Imperial College Press
Published on 28. January 2005
Book
Hardback
184 pages
978-1-86094-511-3 (ISBN)
Description
A new approach to the character theory of the symmetric group has been developed during the past fifteen years which is in many ways more efficient, more transparent, and more elementary. In this approach, to each permutation is assigned a class function of the corresponding symmetric group. Problems in character theory can thereby be transferred into a completely different setting and reduced to combinatorial problems on permutations in a natural and uniform way.This is the first account in book form entirely devoted to the new "noncommutative method". As a modern and comprehensive survey of the classical theory the book contains such fundamental results as the Murnaghan-Nakayama and Littlewood-Richardson rules as well as more recent applications in enumerative combinatorics and in the theory of the free Lie algebra. But it is also an introduction to the vibrant theory of certain combinatorial Hopf algebras such as the Malvenuto-Reutenauer algebra of permutations.The three detailed appendices on group characters, the Solomon descent algebra and the Robinson-Schensted correspondence makes the material self-contained and suitable for undergraduate level. Students and researchers alike will find that noncommutative character theory is a source of inspiration and an illuminating approach to this versatile field of algebraic combinatorics.
Reviews / Votes
"Three appendices make this book self-contained, as no knowledge of the classical theory is assumed. Therefore, this volume is highly recommended to researchers and students alike." Zentralblatt MATHMore details
Language
English
Place of publication
London
United Kingdom
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 237 mm
Width: 164 mm
Thickness: 15 mm
Weight
413 gr
ISBN-13
978-1-86094-511-3 (9781860945113)
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Schweitzer Classification
Persons
Author
Christian-albrechts-univ Kiel, Germany
Univ Of Wales Swansea, Uk
Content
The Inductive Method Noncommutative Character Theory of the Symmetric Group Classical Character Theory of the Symmetric Group Appendices: Elements of Representation Theory Solomon's Mackey Formula Young Tableaux and Knuth Relations