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Representations of the Infinite Symmetric Group Vital Source e-bog
Alexei Borodin og Grigori Olshanski
(2016)
Cambridge University Press
738,00 kr.
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Søgbar e-bog
Representations of the Infinite Symmetric Group Vital Source e-bog
Alexei Borodin og Grigori Olshanski
(2016)
Cambridge University Press
738,00 kr.
Leveres umiddelbart efter køb
Representations of the Infinite Symmetric Group
Alexei Borodin og Grigori Olshanski
(2016)
Sprog: Engelsk
Cambridge University Press
751,00 kr.
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Detaljer om varen
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Cambridge University Press (Oktober 2016)
- Forfattere: Alexei Borodin og Grigori Olshanski
- ISBN: 9781316811894
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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Bookshelf online: 5 år fra købsdato.
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Detaljer om varen
- Vital Source searchable e-book (Fixed pages)
- Udgiver: Cambridge University Press (Oktober 2016)
- Forfattere: Alexei Borodin og Grigori Olshanski
- ISBN: 9781316814628
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.
Licens varighed:
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- Hardback: 168 sider
- Udgiver: Cambridge University Press (Oktober 2016)
- Forfattere: Alexei Borodin og Grigori Olshanski
- ISBN: 9781107175556
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.
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.
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.
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