Representations of Hecke Algebras at Roots of Unity

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9780857297150: Representations of Hecke Algebras at Roots of Unity

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.

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Recensione:

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)

Contenuti:

Generic Iwahori–Hecke algebras.- Kazhdan–Lusztig cells and cellular bases.- Specialisations and decomposition maps.- Hecke algebras and finite groups of Lie type.- Representation theory of Ariki–Koike algebras.- Canonical bases in affine type A and Ariki’s theorem.- Decomposition numbers for exceptional types.

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Descrizione libro Springer, 2011. Hardback. Condizione libro: NEW. 9780857297150 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0286459

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Descrizione libro Springer London Ltd, United Kingdom, 2011. Hardback. Condizione libro: New. 2011. 234 x 160 mm. Language: English . Brand New 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. Codice libro della libreria AAS9780857297150

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Meinolf Geck, Nicolas Jacon
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Descrizione libro Springer London Ltd, United Kingdom, 2011. Hardback. Condizione libro: New. 2011. 234 x 160 mm. Language: English . Brand New 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. Codice libro della libreria AAS9780857297150

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Geck, Meinolf; Jacon, Nicolas
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Descrizione libro Springer, 2011. Hardcover. Condizione libro: New. book. Codice libro della libreria 0857297155

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Descrizione libro Springer, Berlin, 2011. Hardcover. Condizione libro: Brand New. 413 pages. 9.00x6.00x1.00 inches. In Stock. Codice libro della libreria z-0857297155

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