## Spectral Theory of Random MatricesSpectral Theory of Random Matrices |

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An excellent text.

One of the best on the subject.

Very clear, well set out, and very well explained.

### Contents

Chapter 1 Algebras modules and representations | 1 |

Chapter 2 Group representations and characters | 13 |

Chapter 3 Characters and integrality | 33 |

Chapter 4 Products of characters | 47 |

Chapter 5 Induced characters | 62 |

Chapter 6 Normal subgroups | 78 |

Chapter 7 TI sets and exceptional characters | 99 |

Chapter 8 Brauers theorem | 126 |

Chapter 11 Projective representations | 174 |

Chapter 12 Character degrees | 198 |

Chapter 13 Character correspondence | 219 |

Chapter 14 Linear groups | 240 |

Chapter 15 Changing the characteristic | 262 |

Appendix Some character tables | 287 |

Bibliographic notes | 292 |

295 | |

### Common terms and phrases

9 e Irr(N absolutely irreducible afforded algebraic integer Bl(G Brauer character character of G character table character theory character triple class function classes of G conclude conjugacy classes conjugate constituent of 9 COROLLARY Let coset cyclic defined elements exists F-algebra F-representation of G F[G]-module finite Frobenius group G and let g e G G is solvable Galois group G H G G hence homomorphism IBr(G invariant in G Irr(C Irr(H Irr(K irreducible characters irreducible constituent irreducible F-representation isomorphism LEMMA Let Let 9 Let F Let G Let H linear character linear group matrix module nilpotent nonabelian normal subgroup Note p-block p-group permutation Problem projective representations proof is complete Proof Let prove result follows root of unity S-invariant Show that G splitting field subgroup of G Sylow p-subgroup THEOREM Let unique write x e G Ye Irr(G yields