00000cmm a22000004a 4500 UP-99796217611212517 Buklod 20230215085534.0 m go j cr |n |||auu|a 110518s2011 xxk u | eng d 9780857297167 (eBook) 0857297163 (eBook) (iLib)UPD-00215704308 DLC DML eng DMLUC QA 179 G43 2011eb Geck, Meinolf. Representations of Hecke Algebras at Roots of Unity [electronic resource] Meinolf Geck, Nicolas Jacon. London New York Springer c2011. 1 online resource (xii, 401 p.) Algebra and applications 15 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. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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. Electronic reproduction. New York Springerlink 2011. Available via World Wide Web through SpringerLink. Hecke algebras. Representations of algebras. Electronic books. Jacon, Nicolas. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://link.springer.com/book/10.1007/978-0-85729-716-7 FO Monograph UPD DMLR Electronic Resource