Blocks and families for cyclotomic Hecke algebras / Maria Chlouveraki

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. In particular, it corrects the earlier results obtained by S. Kim [J. Algebra 289, No. 2, 346-364 (2005; Zbl 1073.20002)] for the infinite series of type G(de,e,n). The key ingredients in the proof are the notion of “essential" hyperplanes and the property of “semi-continuity".

This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can serve as an introduction to people who want to work in this area. (Zentralblatt)