Representation Theory And Harmonic Analysis Of Wreath Products Of Finite Groups
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| Author | : Tullio Ceccherini-Silberstein |
| Publisher | : Cambridge University Press |
| Total Pages | : 177 |
| Release | : 2014-01-16 |
| Genre | : Mathematics |
| ISBN | : 1107729912 |
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.
| Author | : Tullio Ceccherini-Silberstein |
| Publisher | : Cambridge University Press |
| Total Pages | : 177 |
| Release | : 2014-01-16 |
| Genre | : Mathematics |
| ISBN | : 1107627850 |
A self-contained introduction to the representation theory and harmonic analysis of wreath products of finite groups, with examples and exercises.
| Author | : Pierre-Loic Meliot |
| Publisher | : CRC Press |
| Total Pages | : 567 |
| Release | : 2017-05-12 |
| Genre | : Mathematics |
| ISBN | : 1315353857 |
Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.
| Author | : Tullio Ceccherini-Silberstein |
| Publisher | : Cambridge University Press |
| Total Pages | : 589 |
| Release | : 2018-06-21 |
| Genre | : Mathematics |
| ISBN | : 1107182336 |
A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
| Author | : Grant Walker |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2017-11-09 |
| Genre | : Mathematics |
| ISBN | : 1108355927 |
This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
| Author | : Grant Walker (Mathematician) |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2018 |
| Genre | : Polynomials |
| ISBN | : 1108414451 |
This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
| Author | : Matthias Keller |
| Publisher | : Cambridge University Press |
| Total Pages | : 493 |
| Release | : 2020-08-20 |
| Genre | : Mathematics |
| ISBN | : 1108587380 |
This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.
| Author | : Thierry Daudé |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2018-01-11 |
| Genre | : Science |
| ISBN | : 1108500781 |
This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity. Accessible to graduate students, these notes gather results that were not previously available in textbooks or monographs and will be of wider interest to researchers in general relativity. The topics of these mini courses are: the geometry of black hole spacetimes; an introduction to quantum field theory on curved spacetimes; conformal geometry and tractor calculus; and microlocal analysis for wave propagation.
| Author | : Peter H. Kropholler |
| Publisher | : Cambridge University Press |
| Total Pages | : 277 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 131662322X |
Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.
| Author | : Howard S. Cohl |
| Publisher | : Cambridge University Press |
| Total Pages | : 352 |
| Release | : 2020-10-15 |
| Genre | : Mathematics |
| ISBN | : 1108905420 |
Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.
