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Representation theory and harmonic analysis of wreath products of finite groups /
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 formulati...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2014.
|
| Colección: | London Mathematical Society lecture note series ;
410. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Ceccherini-Silberstein, Tullio, |e author. | |
| 245 | 1 | 0 | |a Representation theory and harmonic analysis of wreath products of finite groups / |c Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2014. | |
| 300 | |a 1 online resource (xii, 163 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 410 | |
| 504 | |a Includes bibliographical references (pages 157-160) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |6 880-01 |a 1. General theory: 1.1. Induced representations; 1.1.1. Definitions; 1.1.2. Transitivity and additivity of induction; 1.1.3. Frobenius character formula; 1.1.4. Induction and restriction; 1.1.5. Induced representations and induced operators; 1.1.6. Frobenius reciprocity; 1.2. Harmonic analysis on a finite homogeneous space; 1.2.1. Frobenius reciprocity for permutation representations; 1.2.2. Spherical functions; 1.2.3. The other side of Frobenius reciprocity for permutation representations; 1.2.4. Gelfand pairs; 1.3. Clifford theory; 1.3.1. Clifford correspondence; 1.3.2. The little group method; 1.3.3. Semidirect products; 1.3.4. Semidirect products with an Abelian normal subgroup; 1.3.5. The affine group over a finite field; 1.3.6. The finite Heisenberg group -- 2. Wreath products of finite groups and their representation theory: 2.1. Basic properties of wreath products of finite groups; 2.1.1. Definitions; 2.1.2. Composition and exponentiation actions; 2.1.3. Iterated wreath products and their actions on rooted trees; 2.1.4. Spherically homogeneous rooted trees and their automorphism group; 2.1.5. The finite ultrametric space; 2.2. Two applications of wreath products to group theory2.2.1. The theorem of Kaloujnine and Krasner; 2.2.2. Primitivity of the exponentiation action; 2.3. Conjugacy classes of wreath products; 2.3.1. A general description of conjugacy classes; 2.3.2. Conjugacy classes of groups of the form C[sub(2)] wr G; 2.3.3. Conjugacy classes of groups of the form F wr S[sub(n)]; 2.4. Representation theory of wreath products; 2.4.1. The irreducible representations of wreath products; 2.4.2. The character and matrix coefficients of the representation tilde sigma. | |
| 505 | 8 | |a 2.5. Representation theory of groups of the form C[sub(2)] wr G2.5.1 Representation theory of the finite lamplighter group C[sub(2)] wr C[sub(n)]; 2.5.2. Representation theory of the hyperoctahedral group C[sub(2)] wr S[sub(n)]; 2.6. Representation theory of groups of the form F wr S[sub(n)]; 2.6.1. Representation theory of S[sub(m)] wr S[sub(n)] -- 3. Harmonic analysis on some homogeneous spaces of finite wreath products: 3.1. Harmonic analysis on the composition of two permutation representations; 3.1.1. Decomposition into irreducible representations; 3.1.2. Spherical matrix coefficients; 8 3.2. The generalized Johnson scheme; 3.2.1. The Johnson scheme; 3.2.2. The homogeneous space Theta h; 3.2.3. Two special kinds of tensor product; 3.2.4. The decomposition of L (Theta [sub(h)]) into irreducible representations; 3.2.5. The spherical functions; 3.2.6. The homogeneous space V(r, s) and the associated Gelfand pair; 3.3. Harmonic analysis on exponentiations and on wreath products of permutation representations; 3.3.1. Exponentiation and wreath products; 3.3.2. The case G=C[sub(2)] and Z trivial; 3.3.3. The case when L(Y) is multiplicity free; 3.3.4. Exponentiation of finite Gelfand pairs; 3.4. Harmonic analysis on finite lamplighter spaces; 3.4.1. Finite lamplighter spaces; 3.4.2. Spectral analysis of an invariant graphs; 3.4.4. The lamplighter on the complete graph. | |
| 520 | |a 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. | ||
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Harmonic analysis. | |
| 650 | 0 | |a Finite groups. | |
| 650 | 2 | |a Fourier Analysis | |
| 650 | 6 | |a Analyse harmonique. | |
| 650 | 6 | |a Groupes finis. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Finite groups. |2 fast |0 (OCoLC)fst00924908 | |
| 650 | 7 | |a Harmonic analysis. |2 fast |0 (OCoLC)fst00951490 | |
| 700 | 1 | |a Scarabotti, Fabio, |e author. | |
| 700 | 1 | |a Tolli, Filippo, |d 1968- |e author. | |
| 776 | 0 | 8 | |i Print version: |a Ceccherini-Silberstein, Tullio. |t Representation theory and harmonic analysis of wreath products of finite groups |z 9781107627857 |w (DLC) 2013024946 |w (OCoLC)853113607 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 410. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=685305 |z Texto completo |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g 1. |t General theory -- |g 1.1. |t Induced representations -- |g 1.1.1. |t Definitions -- |g 1.1.2. |t Transitivity and additivity of induction -- |g 1.1.3. |t Frobenius character formula -- |g 1.1.4. |t Induction and restriction -- |g 1.1.5. |t Induced representations and induced operators -- |g 1.1.6. |t Frobenius reciprocity -- |g 1.2. |t Harmonic analysis on a finite homogeneous space -- |g 1.2.1. |t Frobenius reciprocity for permutation representations -- |g 1.2.2. |t Spherical functions -- |g 1.2.3. |t other side of Frobenius reciprocity for permutation representations -- |g 1.2.4. |t Gelfand pairs -- |g 1.3. |t Clifford theory -- |g 1.3.1. |t Clifford correspondence -- |g 1.3.2. |t little group method -- |g 1.3.3. |t Semidirect products -- |g 1.3.4. |t Semidirect products with an Abelian normal subgroup -- |g 1.3.5. |t affine group over a finite field -- |g 1.3.6. |t finite Heisenberg group -- |g 2. |t Wreath products of finite groups and their representation theory -- |g 2.1. |t Basic properties of wreath products of finite groups -- |g 2.1.1. |t Definitions -- |g 2.1.2. |t Composition and exponentiation actions -- |g 2.1.3. |t Iterated wreath products and their actions on rooted trees -- |g 2.1.4. |t Spherically homogeneous rooted trees and their automorphism group -- |g 2.1.5. |t finite ultrametric space -- |g 2.2. |t Two applications of wreath products to group theory -- |g 2.2.1. |t theorem of Kaloujnine and Krasner -- |g 2.2.2. |t Primitivity of the exponentiation action -- |g 2.3. |t Conjugacy classes of wreath products -- |g 2.3.1. |t general description of conjugacy classes -- |g 2.3.2. |t Conjugacy classes of groups of the form C2 G -- |g 2.3.3. |t Conjugacy classes of groups of the form F Sn -- |g 2.4. |t Representation theory of wreath products -- |g 2.4.1. |t irreducible representations of wreath products -- |g 2.4.2. |t character and matrix coefficients of the representation σ -- |g 2.5. |t Representation theory of groups of the form C2 G -- |g 2.5.1. |t Representation theory of the finite lamplighter group C2 Cn -- |g 2.5.2. |t Representation theory of the hyperoctahedral group C2 Sn -- |g 2.6. |t Representation theory of groups of the form F Sn -- |g 2.6.1. |t Representation theory of Sm Sn -- |g 3. |t Harmonic analysis on some homogeneous spaces of finite wreath products -- |g 3.1. |t Harmonic analysis on the composition of two permutation representations -- |g 3.1.1. |t Decomposition into irreducible representations -- |g 3.1.2. |t Spherical matrix coefficients -- |g 3.2. |t generalized Johnson scheme -- |g 3.2.1. |t Johnson scheme -- |g 3.2.2. |t homogeneous space h -- |g 3.2.3. |t Two special kinds of tensor product -- |g 3.2.4. |t decomposition of L(h) into irreducible representations -- |g 3.2.5. |t spherical functions -- |g 3.2.6. |t homogeneous space V(r, s) and the associated Gelfand pair -- |g 3.3. |t Harmonic analysis on exponentiations and on wreath products of permutation representations -- |g 3.3.1. |t Exponentiation and wreath products -- |g 3.3.2. |t case G = C2 and Z trivial -- |g 3.3.3. |t case when L(Y) is multiplicity free -- |g 3.3.4. |t Exponentiation of finite Gelfand pairs -- |g 3.4. |t Harmonic analysis on finite lamplighter spaces -- |g 3.4.1. |t Finite lamplighter spaces -- |g 3.4.2. |t Spectral analysis of an invariant operator -- |g 3.4.3. |t Spectral analysis of lamplighter graphs -- |g 3.4.4. |t lamplighter on the complete graph. |
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