Blocks and Families for Cyclotomic Hecke Algebras

ISBN-13: 9783642030635 / Angielski / Miękka / 2009 / 166 str.

Maria Chlouveraki

Opis

This book contains a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Cli?ord theory. It can also serve as an introduction to the Hecke algebras of complex re?ection groups. Its aim is the study of the blocks and the determination of the families of characters of the cyclotomic Hecke algebras associated to complex re?ection groups. Iwouldliketothankmythesisadvisor, MichelBrou e, forhisadvice.These Springer Lecture Notes were, after all, his idea. I am grateful to Jean Michel for his help with the implementation and presentation of the programming part. I would like to thank Gunter Malle for his suggestion that I generalize my results on Hecke algebras, which led to the notion of essential algebras . I also express my thanks to C edric Bonnaf e, Meinolf Geck, Nicolas Jacon, Rapha] el Rouquier and Jacques Th evenaz for their useful comments. Finally, I thank Thanos Tsouanas for copy-editing this manuscript. v Introduction The ?nite groups of matrices with coe?cients in Q generated by re?ections, known as Weyl groups, are a fundamental building block in the classi?cation of semisimple complex Lie algebras and Lie groups, as well as semisimple algebraic groups over arbitrary algebraically closed ?elds. They are also a foundation for many other signi?cant mathematical theories, including braid groups and Hecke algebras."

Spis treści

On Commutative Algebra.- On Blocks.- On Essential Algebras.- On Hecke Algebras.- On the Determination of the Rouquier Blocks.

Blurb

The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups. The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups.
This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups.