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Science/Engineering Noncommutative Character Theory Of The Symmetric Group

Posted on 2010-03-16




Name:Science/Engineering Noncommutative Character Theory Of The Symmetric Group
ASIN/ISBN:1860945112
Language:English
File size:5.2 Mb
Publish Date: 2005
ISBN: 1860945112
Pages: 172 pages
File Type: PDF
File Size: 5,2 MB
Other Info: Imperial College Press
   Science/Engineering Noncommutative Character Theory Of The Symmetric Group

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Dieter Blessenohl, Manfred Schocker, "Noncommutative Character Theory Of The Symmetric Group"

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 read.freeduan.com 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.

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