Fabio Scarabotti's Books

Representation Theory of the Symmetric Groups

The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Representation Theory of the Symmetric Groups

The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood–Richardson rule and the Schur–Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle's character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics.

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Page Count

429

Publisher

Cambridge University Press

Published Date

ISBN 10

113948396X

ISBN 13

9781139483964

Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

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Page Count

589

Publisher

Cambridge University Press

Published Date

ISBN 10

1107182336

ISBN 13

9781107182332

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers.

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Page Count

177

Publisher

Cambridge University Press

Published Date

ISBN 10

1107729912

ISBN 13

9781107729919

Gelfand Triples and Their Hecke Algebras

Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Gelfand Triples and Their Hecke Algebras

Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs. Up to now, researchers have been somehow reluctant to face such a problem in a general situation, and only partial results were obtained in the one-dimensional case. Here, for the first time, new interesting and important results are proved. In particular, after developing a general theory (including the study of the associated Hecke algebras and the harmonic analysis of the corresponding spherical functions), two completely new highly nontrivial and significant examples (in the setting of linear groups over finite fields) are examined in full detail. The readership ranges from graduate students to experienced researchers in Representation Theory and Harmonic Analysis.

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Page Count

153

Publisher

Springer Nature

Published Date

ISBN 10

3030516075

ISBN 13

9783030516079

Representation Theory of Finite Group Extensions

Clifford Theory, Mackey Obstruction, and the Orbit Method

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Representation Theory of Finite Group Extensions

Clifford Theory, Mackey Obstruction, and the Orbit Method

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

This monograph adopts an operational and functional analytic approach to the following problem: given a short exact sequence (group extension) 1 → N → G → H → 1 of finite groups, describe the irreducible representations of G by means of the structure of the group extension. This problem has attracted many mathematicians, including I. Schur, A.H. Clifford, and G. Mackey and, more recently, M. Isaacs, B. Huppert, Y.G. Berkovich & E.M. Zhmud, and J.M.G. Fell & R.S. Doran. The main topics are, on the one hand, Clifford Theory and the Little Group Method (of Mackey and Wigner) for induced representations, and, on the other hand, Kirillov’s Orbit Method (for step-2 nilpotent groups of odd order) which establishes a natural and powerful correspondence between Lie rings and nilpotent groups. As an application, a detailed description is given of the representation theory of the alternating groups, of metacyclic, quaternionic, dihedral groups, and of the (finite) Heisenberg group. The Little Group Method may be applied if and only if a suitable unitary 2-cocycle (the Mackey obstruction) is trivial. To overcome this obstacle, (unitary) projective representations are introduced and corresponding Mackey and Clifford theories are developed. The commutant of an induced representation and the relative Hecke algebra is also examined. Finally, there is a comprehensive exposition of the theory of projective representations for finite Abelian groups which is applied to obtain a complete description of the irreducible representations of finite metabelian groups of odd order.

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Page Count

347

Publisher

Springer Nature

Published Date

ISBN 10

3031138732

ISBN 13

9783031138737

Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.

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Page Count

589

Publisher

Cambridge University Press

Published Date

ISBN 10

1316863654

ISBN 13

9781316863657

Representation Theory of the Symmetric Groups

The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Representation Theory of the Symmetric Groups

The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood-Richardson rule and the Schur-Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle's character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics.

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Page Count

430

Publisher

Cambridge University Press

Published Date

ISBN 10

0521118174

ISBN 13

9780521118170

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

By: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

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Solve jigsaw puzzle

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Page Count

177

Publisher

Cambridge University Press

Published Date

ISBN 10

1107729912

ISBN 13

9781107729919

Book's by Fabio Scarabotti

Representation Theory of the Symmetric Groups

Representation Theory of the Symmetric Groups

Discrete Harmonic Analysis

Discrete Harmonic Analysis

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Gelfand Triples and Their Hecke Algebras

Gelfand Triples and Their Hecke Algebras

Representation Theory of Finite Group Extensions

Representation Theory of Finite Group Extensions

Discrete Harmonic Analysis

Discrete Harmonic Analysis

Representation Theory of the Symmetric Groups

Representation Theory of the Symmetric Groups

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

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