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Representations of the infinite symm...

Borodin, Alexei.

Representations of the infinite symmetric group

Record Type:	Electronic resources : Monograph/item
Title/Author:	Representations of the infinite symmetric groupAlexei Borodin, Grigori Olshanski.
Author:	Borodin, Alexei.
other author:	Olshanskii, Grigori
Published:	Cambridge :Cambridge University Press,2017.
Description:	vii, 160 p. :ill., digital ;24 cm.
Subject:	Hopf algebras.
Online resource:	https://doi.org/10.1017/CBO9781316798577
ISBN:	9781316798577$q(electronic bk.)

Representations of the infinite symmetric group
Borodin, Alexei.

Representations of the infinite symmetric group[electronic resource] /Alexei Borodin, Grigori Olshanski. - Cambridge :Cambridge University Press,2017. - vii, 160 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;160. - Cambridge studies in advanced mathematics ;105..

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.

ISBN: 9781316798577$q(electronic bk.)Subjects--Topical Terms:

190853
Hopf algebras.

LC Class. No.: QA613.8 / .B67 2017

Dewey Class. No.: 515.22

Representations of the infinite symmetric group
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100 1 $a Borodin, Alexei. $3 840454
245 1 0 $a Representations of the infinite symmetric group $h [electronic resource] / $c Alexei Borodin, Grigori Olshanski.
260 $a Cambridge : $b Cambridge University Press, $c 2017.
300 $a vii, 160 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 160
520 $a 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.
650 0 $a Hopf algebras. $3 190853
650 0 $a Algebraic topology. $3 189702
650 0 $a Representations of groups. $3 191076
650 0 $a Symmetry groups. $3 185805
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830 0 $a Cambridge studies in advanced mathematics ; $v 105. $3 541725
856 4 0 $u https://doi.org/10.1017/CBO9781316798577