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Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis

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Hardcover ISBN: 978-0-8218-3440-4
Product Code: MMONO/219
List Price: $100.00 MAA Member Price:$90.00
AMS Member Price: $80.00 Electronic ISBN: 978-1-4704-4643-7 Product Code: MMONO/219.E List Price:$94.00
MAA Member Price: $84.60 AMS Member Price:$75.20
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List Price: $150.00 MAA Member Price:$135.00
AMS Member Price: $120.00 Click above image for expanded view Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis Available Formats:  Hardcover ISBN: 978-0-8218-3440-4 Product Code: MMONO/219  List Price:$100.00 MAA Member Price: $90.00 AMS Member Price:$80.00
 Electronic ISBN: 978-1-4704-4643-7 Product Code: MMONO/219.E
 List Price: $94.00 MAA Member Price:$84.60 AMS Member Price: $75.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$150.00 MAA Member Price: $135.00 AMS Member Price:$120.00
• Book Details

Translations of Mathematical Monographs
Volume: 2192003; 201 pp
MSC: Primary 20; 22;

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. In it, he gives a clear and lucid account of results and methods of asymptotic representation theory. The book is a unique source of information on the 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.

Graduate students and research mathematicians interested in representation theory and combinatorics.

• Chapters
• Introduction
• Boundaries and dimension groups of certain graphs
• The boundary of the Young graph and MacDonald polynomials
• The Plancherel measure of the symmetric group
• Young diagrams in problems of analysis

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2192003; 201 pp
MSC: Primary 20; 22;

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. In it, he gives a clear and lucid account of results and methods of asymptotic representation theory. The book is a unique source of information on the 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.