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Universitext

A Journey Through Representation Theory

From Finite Groups to Quivers via Algebras

Authors: Gruson, Caroline, Serganova, Vera

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  • Contains an application of quivers to the Harish-Chandra modules for SL(2)
  • Focuses on representations of finite groups 
  • Includes expositions of the theory of representations of quivers along with substatial material on continuous groups
  • Introduces more advanced topics, such as representations of quantum groups and representations over non-Archimedean local fields, in an elementary way that is accessible to students
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eBook $39.99
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  • ISBN 978-3-319-98271-7
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Softcover $54.99
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  • ISBN 978-3-319-98269-4
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  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

Caroline Gruson is Professor of Mathematics at Université de Lorraine.

Vera Serganova is Professor of Mathematics at University of California, Berkeley. 

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Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-98271-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-98269-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Journey Through Representation Theory
Book Subtitle
From Finite Groups to Quivers via Algebras
Authors
Series Title
Universitext
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-98271-7
DOI
10.1007/978-3-319-98271-7
Softcover ISBN
978-3-319-98269-4
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIII, 223
Topics