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Algebra and Applications

Representations of SL2(Fq)

Authors: Bonnafé, Cédric

  • Presents an introduction to ordinary and modular Deligne-Lusztig theory through the detailed study of an example: SL2(Fq)
  • Will serve as a complementary text to existing titles on Deligne-Lusztig theory
  • Includes Rouquier's theorem on derived equivalences of geometric nature (with some unpublished improvements) but is simple enough to be read by graduate/PhD students
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eBook $69.99
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  • ISBN 978-0-85729-157-8
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Hardcover $99.00
price for USA
  • ISBN 978-0-85729-156-1
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  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
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  • ISBN 978-1-4471-2599-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this Textbook

Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provide the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects.

The development of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups.

At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. With the provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well as researchers and lecturers with an interest in Deligne-Lusztig theory.

Table of contents (12 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-85729-157-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-0-85729-156-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-1-4471-2599-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Representations of SL2(Fq)
Authors
Series Title
Algebra and Applications
Series Volume
13
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-157-8
DOI
10.1007/978-0-85729-157-8
Hardcover ISBN
978-0-85729-156-1
Softcover ISBN
978-1-4471-2599-0
Series ISSN
1572-5553
Edition Number
1
Number of Pages
XXII, 186
Topics