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BOOK EXCERPT:
Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.
Product Details :
Genre |
: Mathematics |
Author |
: Pierre-Loic Meliot |
Publisher |
: CRC Press |
Release |
: 2017-05-12 |
File |
: 433 Pages |
ISBN-13 |
: 9781315353852 |
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BOOK EXCERPT:
The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood–Richardson rule and the Schur–Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle's character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics.
Product Details :
Genre |
: Mathematics |
Author |
: Tullio Ceccherini-Silberstein |
Publisher |
: Cambridge University Press |
Release |
: 2010-02-04 |
File |
: 429 Pages |
ISBN-13 |
: 9781139483964 |
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BOOK EXCERPT:
Product Details :
Genre |
: Mathematics |
Author |
: G.D. James |
Publisher |
: Springer |
Release |
: 2006-11-15 |
File |
: 162 Pages |
ISBN-13 |
: 9783540357117 |
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BOOK EXCERPT:
Kleshchev describes a new approach to the subject of the representation theory of symmetric groups.
Product Details :
Genre |
: Mathematics |
Author |
: Aleksandr Sergeevich Kleshchëv |
Publisher |
: Cambridge University Press |
Release |
: 2005-06-30 |
File |
: 304 Pages |
ISBN-13 |
: 0521837030 |
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BOOK EXCERPT:
Product Details :
Genre |
: Mathematics |
Author |
: Donald Knutson |
Publisher |
: Springer |
Release |
: 2006-11-15 |
File |
: 208 Pages |
ISBN-13 |
: 9783540384083 |
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BOOK EXCERPT:
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.
Product Details :
Genre |
: Mathematics |
Author |
: Aleksandr Sergeevich Kleshchëv |
Publisher |
: American Mathematical Soc. |
Release |
: 2012 |
File |
: 148 Pages |
ISBN-13 |
: 9780821874318 |
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BOOK EXCERPT:
Introducing the representation theory of finite groups, this second edition has been revised and updated. The theory is developed in terms of modules with considerable emphasis placed upon constructing characters.
Product Details :
Genre |
: Mathematics |
Author |
: Gordon Douglas James |
Publisher |
: Cambridge University Press |
Release |
: 2001-10-18 |
File |
: 476 Pages |
ISBN-13 |
: 052100392X |
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BOOK EXCERPT:
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Product Details :
Genre |
: Mathematics |
Author |
: Alexei Borodin |
Publisher |
: Cambridge University Press |
Release |
: 2017 |
File |
: 169 Pages |
ISBN-13 |
: 9781107175556 |
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BOOK EXCERPT:
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./a
Product Details :
Genre |
: Mathematics |
Author |
: Dieter Blessenohl |
Publisher |
: World Scientific |
Release |
: 2005-01-27 |
File |
: 184 Pages |
ISBN-13 |
: 9781911299127 |
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BOOK EXCERPT:
This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH
Product Details :
Genre |
: Mathematics |
Author |
: Bruce E. Sagan |
Publisher |
: Springer Science & Business Media |
Release |
: 2013-03-09 |
File |
: 254 Pages |
ISBN-13 |
: 9781475768046 |