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A Journey Through Representation Theory

From Finite Groups to Quivers via Algebras

  • Caroline Gruson
  • Vera Serganova

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Caroline Gruson, Vera Serganova
    Pages 1-23
  3. Caroline Gruson, Vera Serganova
    Pages 25-46
  4. Caroline Gruson, Vera Serganova
    Pages 47-63
  5. Caroline Gruson, Vera Serganova
    Pages 65-80
  6. Caroline Gruson, Vera Serganova
    Pages 81-104
  7. Caroline Gruson, Vera Serganova
    Pages 149-168
  8. Caroline Gruson, Vera Serganova
    Pages 169-191
  9. Caroline Gruson, Vera Serganova
    Pages 193-217
  10. Back Matter
    Pages 219-223

About this book

Introduction

This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. 

The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras.  The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter.

Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.

Keywords

Artinian rings Peter-Weyl theorem continuous groups representation theory of finite groups representations of algebras representations of quivers invariant forms Orthogonality relations Harish-Chandra modules application quivers textbook representation theory graduate mathematics text Schur-Weyl duality self-adjoint Hopf algebras SL(2) modules

Authors and affiliations

  • Caroline Gruson
    • 1
  • Vera Serganova
    • 2
  1. 1.Institut Elie Cartan, UMR 7502 du CNRSUniversité de Lorraine, CNRS, IESLNancyFrance
  2. 2.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-98271-7
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-98269-4
  • Online ISBN 978-3-319-98271-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site