Representations of the Infinite Symmetric Group

Nonfiction, Science & Nature, Mathematics, Algebra, Science
Cover of the book Representations of the Infinite Symmetric Group by Alexei Borodin, Grigori Olshanski, Cambridge University Press
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Author: Alexei Borodin, Grigori Olshanski ISBN: 9781316811894
Publisher: Cambridge University Press Publication: October 27, 2016
Imprint: Cambridge University Press Language: English
Author: Alexei Borodin, Grigori Olshanski
ISBN: 9781316811894
Publisher: Cambridge University Press
Publication: October 27, 2016
Imprint: Cambridge University Press
Language: English

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.

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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.

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