scholarly journals Blocks and Families for Cyclotomic Hecke Algebras

2009 ◽  
Author(s):  
Maria Chlouveraki
Keyword(s):  
Hecke Algebras ◽  
Cyclotomic Hecke Algebras

scholarly journals Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r)

2010 ◽  
Vol 197 ◽  
pp. 175-212
Author(s):  
Maria Chlouveraki
Keyword(s):  
Infinite Series ◽  
Hecke Algebras ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Cyclotomic Hecke Algebras

The Rouquier blocks of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the families of characters defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite seriesG(de, e, r), thus completing their calculation for all complex reflection groups.

scholarly journals Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r)

2010 ◽  
Vol 197 ◽  
pp. 175-212 ◽  
Author(s):  
Maria Chlouveraki
Keyword(s):  
Infinite Series ◽  
Hecke Algebras ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Cyclotomic Hecke Algebras

The Rouquier blocks of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the families of characters defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite series G(de, e, r), thus completing their calculation for all complex reflection groups.

scholarly journals SCHUR ELEMENTS AND BASIC SETS FOR CYCLOTOMIC HECKE ALGEBRAS

2011 ◽  
Vol 10 (05) ◽  
pp. 979-993 ◽  
Author(s):  
MARIA CHLOUVERAKI ◽  
NICOLAS JACON
Keyword(s):  
Hecke Algebras ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Schur Elements ◽  
Basic Sets ◽  
Cyclotomic Hecke Algebras

We study the Schur elements and the a-function for cyclotomic Hecke algebras. As a consequence, we show the existence of canonical basic sets, as defined by Geck–Rouquier, for certain complex reflection groups. This includes the case of finite Weyl groups for all choices of parameters (in characteristic 0).

scholarly journals Decomposition matrices for d-Harish-Chandra series: the exceptional rank two cases

2011 ◽  
Vol 14 ◽  
pp. 271-290 ◽  
Author(s):  
Maria Chlouveraki ◽  
Hyohe Miyachi
Keyword(s):  
Characteristic Zero ◽  
Hecke Algebras ◽  
Irreducible Representations ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Basic Sets ◽  
Cyclotomic Hecke Algebras

AbstractWe calculate all decomposition matrices of the cyclotomic Hecke algebras of the rank two exceptional complex reflection groups in characteristic zero. We prove the existence of canonical basic sets in the sense of Geck–Rouquier and show that all modular irreducible representations can be lifted to the ordinary ones.

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