Decomposition Matrices for the Generic Hecke Algebras on 3 Strands in Characteristic 0

@article{Chavli2019DecompositionMF,
  title={Decomposition Matrices for the Generic Hecke Algebras on 3 Strands in Characteristic 0},
  author={Eirini Chavli},
  journal={Algebras and Representation Theory},
  year={2019},
  volume={23},
  pages={1001-1030}
}
  • Eirini Chavli
  • Published 30 December 2017
  • Mathematics
  • Algebras and Representation Theory
We determine all the decomposition matrices of the generic Hecke algebras on 3 strands in characteristic 0. These are the generic Hecke algebras associated with the exceptional complex reflection groups G 4 , G 8 , and G 16 . We prove that for every choice of the parameters that define these algebras, all simple representations of the specialized algebra are obtained as modular reductions of simple representations of the generic algebra. 
2 Citations
Representations of Finite-Dimensional Quotient Algebras of the 3-String Braid Group
We consider quotients of the group algebra of the $3$-string braid group $B_3$ by $p$-th order generic polynomial relations on the elementary braids. In cases $p=2,3,4,5$ these quotient algebras are
Defect in cyclotomic Hecke algebras
The complexity of a block of a symmetric algebra can be measured by the notion of defect, a numerical datum associated to each of the simple modules contained in the block. Geck showed that the

References

SHOWING 1-10 OF 27 REFERENCES
Constructing representations of Hecke algebras for complex reflection groups
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of
Decomposition matrices for d -Harish-Chandra series: the exceptional rank two cases
We 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
Universal deformations of the finite quotients of the braid group on 3 strands
We prove that the quotients of the group algebra of the braid group on 3 strands by a generic quartic and quintic relation respectively, have finite rank. This is a special case of a conjecture by
Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras
1 CARTAN MATRICES AND FINITE COXETER GROUPS 2 PARABOLIC SUBGROUPS 3 CONJUGACY CLASSES AND SPECIAL ELEMENTS 4 THE BRAID MONOID AND GOOD ELEMENTS 5 IRREDUCIBLE CHARACTERS OF FINITE COXETER GROUPS 6
The BMM symmetrising trace conjecture for groups G4,  G5,  G6,  G7,  G8
Abstract We prove the BMM symmetrising trace conjecture for the exceptional irreducible complex reflection groups G 4 , G 5 , G 6 , G 7 , G 8 using a combination of algorithms programmed in different
Blocks and Families for Cyclotomic Hecke Algebras
These lecture notes study the Rouquier blocks (i.e. the families of characters) of the cyclotomic Hecke algebras. The families of characters are determined for all irreducible complex reflection
Linear representations of finite groups
Representations and characters: generalities on linear representations character theory subgroups, products, induced representation compact groups examples. Representations in characteristic zero:
On the Rationality and Fake Degrees of Characters of Cyclotomic Algebras
Let W be a finite complex reflection group, and H = H(W,u) the corresponding generic (cyclotomic) Hecke algebra as introduced in [8] and [9]. In this paper we study the character fields of the
COMPLEX REFLECTION GROUPS, BRAID GROUPS, HECKE ALGEBRAS
Presentations a la Coxeter are given for all irreducible nite com plex re ection groups They provide presentations for the corresponding generalized braid groups for all but six cases which allow us
Finite Unitary Reflection Groups
Any finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of
...
1
2
3
...