Algebra and Applications

Representations of Hecke Algebras at Roots of Unity

Authors: Geck, Meinolf, Jacon, Nicolas

  • Offers the first systematic and unified treatment of representations of Hecke algebras at roots of unity
  • Written by leading experts in the field
  • Uses a number of concrete examples to clearly explain theoretical results
  • Uses sophisticated mathematical results from Representation Theory  and Combinatorics to describe state of the art developments in Hecke algebra theory
  • Describes the connections between Representation theory of quantum affine algebras and Representation Theory of Hecke algebras
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About this book

The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general.

Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras.

The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods.

This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.

Reviews

From the reviews:

“This book unifies and summaries some of the work, mostly done during the last ten years, on representations of Iwahori-Hecke algebras of finite Coxeter groups. … The book is very nicely written, striking the ideal balance between providing a uniform treatment of the finite Coxeter groups on the one hand, and presenting type-specific material on the other. … In summary, this book is excellent. It will serve primarily as a reference for experts, but would also work well for self-study for a graduate student.” (Matthew Fayers, Zentralblatt MATH, Vol. 1232, 2012)


Table of contents (7 chapters)

  • Generic Iwahori–Hecke Algebras

    Geck, Meinolf (et al.)

    Pages 1-58

  • Kazhdan–Lusztig Cells and Cellular Bases

    Geck, Meinolf (et al.)

    Pages 59-132

  • Specialisations and Decomposition Maps

    Geck, Meinolf (et al.)

    Pages 133-206

  • Hecke Algebras and Finite Groups of Lie Type

    Geck, Meinolf (et al.)

    Pages 207-259

  • Representation Theory of Ariki–Koike Algebras

    Geck, Meinolf (et al.)

    Pages 261-307

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-0-85729-716-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-0-85729-715-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4471-2657-7
  • 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 Hecke Algebras at Roots of Unity
Authors
Series Title
Algebra and Applications
Series Volume
15
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-716-7
DOI
10.1007/978-0-85729-716-7
Hardcover ISBN
978-0-85729-715-0
Softcover ISBN
978-1-4471-2657-7
Series ISSN
1572-5553
Edition Number
1
Number of Pages
XII, 404
Topics