An introduction to the representation theory of groups / Emmanuel Kowalski.

Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as cl...

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Bibliographic Details
Main Author: Kowalski, Emmanuel, 1969- (Author)
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2014]
Series:Graduate studies in mathematics ; v. 155.
Subjects:
Lie groups.
Representations of groups.
Group algebras.
Physical Description:vi, 432 pages : illustrations ; 27 cm.
Format: Book
Contents:
  • Chapter 1: Introduction and motivation
  • Presentation
  • Four motivating statements
  • Prerequisites and notation
  • Chapter 2: The language of representation theory
  • Basic language
  • Formalism: changing the space
  • Formalism: changing the group - Formalism: changing the field
  • Matrix representations
  • Examples
  • Some general results
  • Some Clifford theory
  • Conclusion
  • Chapter 3: Variants
  • Representations of algebras
  • Representations of Lie algebras
  • Topological groups
  • Unitary representations
  • Chapter 4: Linear representations of finite groups
  • Maschke's Theorem
  • Applications of Maschke's Theorem
  • Decomposition of representations
  • Harmonic analysis on finite groups
  • Finite abelian groups
  • The character table
  • Applications
  • Further topics
  • Chapter 5: Abstract representation theory of compact groups
  • An example: the circle group
  • The Haar measure and the regular representation of a locally compact group
  • The analogue of the group algebra
  • The Peter-Weyl Theorem
  • Characters and matrix coefficients for compact gropus
  • Some first examples
  • Chapter 6: Applications of representations of compact groups
  • Compact Lie groups are matrix groups
  • The Frobenius-Schur indicator
  • The Larsen alternative
  • The hydrogen atom
  • Chapter 7: Other groups: a few examples
  • Algebraic groups - Locally compact groups: general remarks
  • Locally compact abelian groups
  • A non-abelian example: SL2(R)
  • Appendix A. Some useful facts. A.1. Algebraic integers
  • A.2. The spectral theorem
  • A.3. The Stone-Weierstrass Theorem.