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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 |
Tabla de Contenidos:
- 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.
- 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.