Cambridge Studies in Advanced Mathematics: Series Number 160: Representations of the Infinite Symmetric Group

Alexei Borodin

ISBN 10: 1107175550 / ISBN 13: 9781107175556

Published by Cambridge University Press, 2016

About this Item

An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics. Series: Cambridge Studies in Advanced Mathematics. Num Pages: 168 pages, 2 b/w illus. 80 exercises. BIC Classification: PBF. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 160 x 236 x 16. Weight in Grams: 380. . 2016. Illustrated. hardcover. . . . .

Seller Inventory # V9781107175556

Bibliographic Details

• Title: Cambridge Studies in Advanced Mathematics: Series Number 160: Representations of the Infinite Symmetric Group
• Publisher: Cambridge University Press
• Publication Date: 2016
• Language: English
• ISBN 10: 1107175550
• ISBN 13: 9781107175556
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

About the Authors

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.