Representations of the infinite symmetric group

By:

Borodin, Alexei

Contributor(s):

Olshanskii, Grigori I

Series: Cambridge studies in advanced mathematics ; 160Publication details: Cambridge University Press, 2017. Cambridge:Description: vii, 160 p. : ill. ; hb, 24 cmISBN:

9781107175556

Subject(s):

DDC classification:

515.22 BOR

Summary: 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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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	515.22 BOR (Browse shelf(Opens below))	1	Available		030159

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Previous	515 TAO Analysis - II	515 VEL Calculus: a rigorous first course	515.1 LIP Geometric analysis	515.22 BOR Representations of the infinite symmetric group	515.2422 MUS Classical and multilinear harmonic analysis, Vol.2	515.243 HIR Infinite series	515.2433 JEN Ripples in mathematics: the discrete wavelet transform	Next

Includes bibliographical references and index.

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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