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Group Matrices, Group Determinants and Representation Theory

The Mathematical Legacy of Frobenius

  • Kenneth W.┬áJohnson
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2233)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Kenneth W. Johnson
    Pages 55-110
  3. Kenneth W. Johnson
    Pages 111-136
  4. Kenneth W. Johnson
    Pages 137-175
  5. Kenneth W. Johnson
    Pages 211-229
  6. Kenneth W. Johnson
    Pages 271-286
  7. Kenneth W. Johnson
    Pages 287-311
  8. Kenneth W. Johnson
    Pages 313-340
  9. Back Matter
    Pages 341-384

About this book

Introduction

This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science.

The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.



Keywords

Group Determinant Group Matrix k-Characters of Groups Norm forms on algebras Association schemes S-rings Fusion of characters Fission of characters Weak Cayley table Fourier transforms Random walks

Authors and affiliations

  • Kenneth W.┬áJohnson
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityAbingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-28300-1
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-28299-8
  • Online ISBN 978-3-030-28300-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site