Representation theory of finite group extensions Cclifford theory, Mackey obstruction, and the orbit method /

Representation theory of finite group extensions [electronic resource] : Cclifford theory, Mackey obstruction, and the orbit method / 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 m...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Ceccherini-Silberstein, Tullio
Other Authors: Scarabotti, Fabio, Tolli, Filippo, 1968-
Format: Electronic eBook
Language:English
Published: Cham, Switzerland : Springer, 2022.
Series:Springer monographs in mathematics.
Subjects:
Representations of groups.
Group theory.
Table of Contents:
  • 2.5 Some Applications of Mackey Theory to Clifford Theory
  • 2.6 The G-Action on the N-Conjugacy Classes
  • 2.7 Real, Complex, and Quaternionic Representations and Clifford Theory
  • 2.8 Semidirect Products with an Abelian Normal Subgroup
  • 2.9 Semidirect Products of Abelian Groups
  • 2.10 Representation Theory of Wreath Products of Finite Groups
  • 2.11 Multiplicity-Free Normal Subgroups
  • 3 Abelian Extensions
  • 3.1 The Dual Action
  • 3.2 The Conjugation Action
  • 3.3 The Intermediary Representations
  • 3.4 Diagrammatic Summaries
  • 4 The Little Group Method for Abelian Extensions.
  • 4.1 General Theory
  • 4.2 Normal Subgroups with the Prime Condition
  • 4.3 Normal Subgroups of Prime Index
  • 4.4 The Case of Index Two Subgroups
  • 5 Examples and Applications
  • 5.1 Representation Theory and Conjugacy Classes of the Symmetric Groups Sn
  • 5.2 Conjugacy Classes of An
  • 5.3 The Irreducible Representations of An
  • 5.4 Ambivalence of the Groups An
  • 5.5 An Application to Isaacs' Going Down Theorem
  • 5.6 Another Application: Analysis of p2-Extensions
  • 5.7 Representation Theory of Finite Metacyclic Groups
  • 5.8 Examples: Dihedral and Generalized Quaternion Groups.
  • 6 Central Extensions and the Orbit Method
  • 6.1 Central Extensions
  • 6.2 2-Divisible Abelian Groups, Equalized Cocycles, and Schur Multipliers
  • 6.3 Lie Rings
  • 6.4 The Cocycle Decomposition
  • 6.5 The Malcev Correspondence
  • 6.6 The Orbit Method
  • 6.7 More on the Orbit Method: Induced Representations
  • 6.8 More on the Orbit Method: Restricting to a Subgroup
  • 6.9 The Orbit Method for the Finite Heisenberg Group
  • 6.10 Restricting from Hqt to Hq
  • 6.11 The Little Group Method for the Heisenberg Group
  • 7 Representations of Finite Group Extensions via Projective Representations.
  • 7.1 Mackey Obstruction
  • 7.2 Unitary Projective Representations
  • 7.3 The Dual of a Group Extension
  • 7.4 Central Extensions and the Finite Heisenberg Group
  • 7.5 Analysis of the Commutant
  • 7.6 The Hecke Algebra
  • 8 Induced Projective Representations
  • 8.1 Basic Theory
  • 8.2 Mackey's Theory for Induced Projective Representations
  • 9 Clifford Theory for Projective Representations
  • 9.1 Preliminaries and Notation
  • 9.2 Basic Clifford Theory for Projective Representations
  • 9.3 Projective Unitary Representations of a Group Extension.

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