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The Symmetric Group

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 044/5 ( reviews)

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Book Synopsis The Symmetric Group by : Bruce E. Sagan

Download or read book The Symmetric Group written by Bruce E. Sagan. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. 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

Representation Theory of Symmetric Groups

2017-05-12 Mathematics
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Release : 2017-05-12
Genre : Mathematics
Kind : eBook
Book Rating : 139/5 ( reviews)

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Book Synopsis Representation Theory of Symmetric Groups by : Pierre-Loic Meliot

Download or read book Representation Theory of Symmetric Groups written by Pierre-Loic Meliot. This book was released on 2017-05-12. Available in PDF, EPUB and Kindle. 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.

The Representation Theory of the Symmetric Group

1984-12-28 Mathematics
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Release : 1984-12-28
Genre : Mathematics
Kind : eBook
Book Rating : 366/5 ( reviews)

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Book Synopsis The Representation Theory of the Symmetric Group by : Gordon Douglas James

Download or read book The Representation Theory of the Symmetric Group written by Gordon Douglas James. This book was released on 1984-12-28. Available in PDF, EPUB and Kindle. Book excerpt: The Representation Theory of the Symmetric Group provides an account of both the ordinary and modular representation theory of the symmetric groups. The range of applications of this theory is vast, varying from theoretical physics, through combinatories to the study of polynomial identity algebras; and new uses are still being found.

Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize

Mathematics
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Genre : Mathematics
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Book Rating : 633/5 ( reviews)

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Book Synopsis Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize by : Sergei Vasilʹevich Kerov

Download or read book Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize written by Sergei Vasilʹevich Kerov. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: This book reproduces the doctoral thesis written by a remarkable mathematician, Sergei V. Kerov. His untimely death at age 54 left the mathematical community with an extensive body of work and this one-of-a-kind monograph. Here, he gives a clear and lucid account of results and methods of asymptotic representation theory. The book is a unique source of information on an important topic of current research. Asymptotic representation theory of symmetric groups deals with problems of two types: asymptotic properties of representations of symmetric groups of large order and representations of the limiting object, i.e., the infinite symmetric group. The author contributed significantly in the development of both directions. His book presents an account of these contributions, as well as those of other researchers. Among the problems of the first type, the author discusses the properties of the distribution of the normalized cycle length in a random permutation and the limiting shape of a random (with respect to the Plancherel measure) Young diagram. He also studies stochastic properties of the deviations of random diagrams from the limiting curve. Among the problems of the second type, Kerov studies an important problem of computing irreducible characters of the infinite symmetric group. This leads to the study of a continuous analog of the notion of Young diagram, and in particular, to a continuous analogue of the hook walk algorithm, which is well known in the combinatorics of finite Young diagrams. In turn, this construction provides a completely new description of the relation between the classical moment problems of Hausdorff and Markov. The book is suitable for graduate students and research mathematicians interested in representation theory and combinatorics.

Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group

1999 Mathematics
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Release : 1999
Genre : Mathematics
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Book Rating : 267/5 ( reviews)

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Book Synopsis Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group by : Andrew Mathas

Download or read book Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group written by Andrew Mathas. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the $q$-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and $q$-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the $q$-Schur algebras. This book is the first of its kind covering the topic. It offers a substantially simplified treatment of the original proofs. The book is a solid reference source for experts. It will also serve as a good introduction to students and beginning researchers since each chapter contains exercises and there is an appendix containing a quick development of the representation theory of algebras. A second appendix gives tables of decomposition numbers.

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