Maria Chlouveraki
Published 2008-07-09, updated 2011-07-18Version 3
The families of characters, defined by Lusztig for Weyl groups, play an important role in the representation theory of finite reductive groups. The definition of Rouquier for the families of characters in terms of blocks of the Hecke algebra has made possible the generalization of this notion to the case of complex reflection groups. In this article, we study the Rouquier blocks of the cyclotomic Hecke algebras and we show that they depend on numerical data determined by the generic Hecke algebra. Moreover, we provide the algorithm and the results of their determination for all exceptional complex reflection groups.
Comments: This article is essentially the work of my Ph.D. thesis. The difference lies in the third chapter, where we introduce the notion of essential algebras and study their blocks. In the second version, 40 more pages were added to cover the groups of the infinite series
On the cyclotomic Hecke algebras of complex reflection groups
Rouquier blocks of the cyclotomic Hecke algebras of G(de,e,r)
Degree and valuation of the Schur elements of cyclotomic Hecke algebras
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