Overview
- 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
Part of the book series: Universitext (UTX)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
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
About this book
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.
Authors and Affiliations
About the authors
Vera Serganova is Professor of Mathematics at University of California, Berkeley.
Bibliographic Information
Book Title: A Journey Through Representation Theory
Book Subtitle: From Finite Groups to Quivers via Algebras
Authors: Caroline Gruson, Vera Serganova
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-98271-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-98269-4Published: 26 October 2018
eBook ISBN: 978-3-319-98271-7Published: 23 October 2018
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIII, 223
Topics: Group Theory and Generalizations