Representations of Hecke Algebras at Roots of Unity

Fulfilling a valuable need in the field, this volume classifies the irreducible representations of Iwahori-Hecke algebras at roots of unity. The text develops an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general.

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.

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 Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt

Generic IwahoriHecke algebras.- KazhdanLusztig cells and cellular bases.- Specialisations and decomposition maps.- Hecke algebras and finite groups of Lie type.- Representation theory of ArikiKoike algebras.- Canonical bases in affine type A and Ariki's theorem.- Decomposition numbers for exceptional types.