Representations of Hecke Algebras at Roots of Unity

1. Front Matter

   Pages I-XII

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2. Generic Iwahori–Hecke Algebras

   • Meinolf Geck, Nicolas Jacon

   Pages 1-58

3. Kazhdan–Lusztig Cells and Cellular Bases

   • Meinolf Geck, Nicolas Jacon

   Pages 59-132

4. Specialisations and Decomposition Maps

   • Meinolf Geck, Nicolas Jacon

   Pages 133-206

5. Hecke Algebras and Finite Groups of Lie Type

   • Meinolf Geck, Nicolas Jacon

   Pages 207-259

6. Representation Theory of Ariki–Koike Algebras

   • Meinolf Geck, Nicolas Jacon

   Pages 261-307

7. Canonical Bases in Affine Type A and Ariki’s Theorem

   • Meinolf Geck, Nicolas Jacon

   Pages 309-361

8. Decomposition Numbers for Exceptional Types

   • Meinolf Geck, Nicolas Jacon

   Pages 363-386

9. Back Matter

   Pages 387-401

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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.

• Canonical bases
• Fock spaces
• Hecke algebras
• Modular representations

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)

• King's College, Department of Mathematical Sciences, University of Aberdeen, Aberdeen, United Kingdom

  Meinolf Geck

• UFR Sciences et Techniques, Université de Franche-Comté, Besancon, France

  Nicolas Jacon

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