Noncommutative Character Theory Of The Symmetric Group
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A01=Dieter Blessenohl
A01=Manfred Schocker
Author_Dieter Blessenohl
Author_Manfred Schocker
Bialgebra
Category=PBG
Category=PBH
Character
Coplactic
Descent
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Hopf Algebra
Permutation
Plactic
Robinson-Schensted Correspondence
Symmetric Group
Young Tableau
Product details
- ISBN 9781860945113
- Publication Date: 28 Jan 2005
- Publisher: Imperial College Press
- Publication City/Country: GB
- Product Form: Hardback
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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.
