Representations of the Infinite Symmetric Group

Inbunden, Engelska, 2016

Del 160 i serien Cambridge Studies in Advanced Mathematics

801 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-10-27
Mått:157 x 235 x 15 mm
Vikt:380 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:168
Förlag:Cambridge University Press
ISBN:9781107175556

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

Alexei Borodin is a Professor of Mathematics at the Massachusetts Institute of Technology. Grigori Olshanski is a Principal Researcher in the Section of Algebra and Number Theory at the Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow. He also holds the position of Dobrushin Professor at the National Research University Higher School of Economics, Moscow.

Recensioner i media

'… 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, Zentralblatt MATH

Innehållsförteckning

Introduction; Part I. Symmetric Functions and Thoma's Theorem: 1. Preliminary facts from representation theory of finite symmetric groups; 2. Theory of symmetric functions; 3. Coherent systems on the Young graph; 4. Extreme characters and Thoma's Theorem; 5. A toy model (the Pascal Graph) and de Finetti's Theorem; 6. Asymptotics of relative dimension in the Young graph; 7. Boundaries and Gibbs measures on paths; Part II. Unitary Representations: 8. Preliminaries and Gelfand pairs; 9. Classification of general spherical type representations; 10. Realization of irreducible spherical representations of (S(∞) × S(∞), diagS(∞)); 11. Generalized regular representations Tz; 12. Disjointness of representations Tz; References; Index.