scholarly journals Complex reflection groups, braid groups, Hecke algebras

1998 ◽  
Vol 1998 (500) ◽  
pp. 127-190 ◽  
Author(s):  
Raphaël Rouquier ◽  
Gunter Malle ◽  
Michel Broué
Keyword(s):  
Hecke Algebras ◽  
Braid Groups ◽  
Reflection Groups ◽  
Complex Reflection ◽  
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 seriesG(de, e, r), thus completing their calculation for all complex reflection groups.

scholarly journals Murnaghan-Nakayama Rules for Characters of Iwahori-Hecke Algebras of the Complex Reflection Groups G(r, p, n)

1998 ◽  
Vol 50 (1) ◽  
pp. 167-192 ◽  
Author(s):  
Tom Halverson ◽  
Arun Ram
Keyword(s):  
Symmetric Group ◽  
Infinite Series ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Diagonal Matrix ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Irreducible Characters ◽  
Complex Reflection ◽  
Complex Reflection Groups

AbstractIwahori-Hecke algebras for the infinite series of complex reflection groups G(r, p, n) were constructed recently in the work of Ariki and Koike [AK], Broué andMalle [BM], and Ariki [Ari]. In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of these algebras. Our method is a generalization of that in our earlier paper [HR] in whichwe derivedMurnaghan-Nakayama rules for the characters of the Iwahori-Hecke algebras of the classical Weyl groups. In both papers we have been motivated by C. Greene [Gre], who gave a new derivation of the Murnaghan-Nakayama formula for irreducible symmetric group characters by summing diagonal matrix entries in Young's seminormal representations. We use the analogous representations of the Iwahori-Hecke algebra of G(r, p, n) given by Ariki and Koike [AK] and Ariki [Ari].

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.

Three-dimensional representations of braid groups associated with some finite complex reflection groups

2017 ◽  
Vol 28 (14) ◽  
pp. 1750109 ◽  
Author(s):  
Yoshishige Haraoka ◽  
Toshiya Matsumura
Keyword(s):  
Three Dimensional ◽  
Braid Groups ◽  
Finite Complex ◽  
Systems Of Equations ◽  
Reflection Groups ◽  
Hermitian Forms ◽  
Complex Reflection ◽  
Complex Reflection Groups

We study the rigidity of three-dimensional representations of braid groups associated with finite primitive irreducible complex reflection groups in [Formula: see text]. In many cases, we show the rigidity. For rigid representations, we give explicit forms of the representations, which turns out to be the monodromy representations of uniformization equations of Saito–Kato–Sekiguchi [Uniformization systems of equations with singularities along the discriminant sets of complex reflection groups of rank three, Kyushu J. Math. 68 (2014) 181–221; On the uniformization of complements of discriminant loci, RIMS Kokyuroku 287 (1977) 117–137]. Invariant Hermitian forms are also studied.

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