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  3. Representations of the Infinite Symmetric Group
  • Cited by 23
Publisher:
Cambridge University Press
Online publication date:
November 2016
Print publication year:
2016
Online ISBN:
9781316798577
DOI:
https://doi.org/10.1017/CBO9781316798577
Subjects:
Mathematics (general), Mathematics, Physics and Astronomy, Theoretical Physics and Mathematical Physics, Algebra
Series:
Cambridge Studies in Advanced Mathematics (160)
Information

Book description

Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas.

Reviews

'… the aim of this book is to provide a detailed introduction to the representation theory of S(∞) in such a way that would be accessible to graduate and advanced undergraduate students. At the end of each section of the book, there are exercises and notes which are helpful for students who choose the book for the course.'

Mohammad-Reza Darafsheh Source: Zentralblatt MATH

'This book by A. Borodin and G. Olshanski is devoted to the representation theory of the infinite symmetric group, which is the inductive limit of the finite symmetric groups and is in a sense the simplest example of an infinite-dimensional group. … This book is the first work on the subject in the format of a conventional book, making the representation theory accessible to graduate students and undergraduates with a solid mathematical background. The book is very well written, with clean and clear exposition, and has a nice collection of exercises to help the engaged reader absorb the material. It does not assume a lot of background material, just some familiarity with the representation theory of finite groups, basic probability theory and certain results from functional analysis. … Among the many useful features of the book are its comprehensive list of references and notes after every section that direct the reader to the relevant literature to further explore the topics discussed.'

Sevak Mkrtchyan Source: Mathematical Reviews

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