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Representations of Finite Groups
No full textThe workshop "Representations of Finite Groups" was organised by Olivier Dudas
(Marseille), Meinolf Geck (Stuttgart), Radha Kessar (Manchester), and Gabriel
Navarro (Valencia). It covered a wide variety of aspects of the representation theory
of finite groups and related topics, and showcased several recent breakthrough results
Representations of Finite Groups
No full textThe workshop Representations of Finite Groups was organised by Joseph Chuang (London), Meinolf Geck (Stuttgart), Radha Kessar (London) and Gabriel Navarro (Valencia). It covered a wide variety of aspects of representation theory of finite groups and its relations to other areas of mathematics
Recommended from our members
Representations of Finite Groups
Get PDFThe workshop Representations of Finite Groups was organised by Joseph Chuang (London), Meinolf Geck (Stuttgart), Radha Kessar (London) and Gabriel Navarro (Valencia). It covered a wide variety of aspects of representation theory of finite groups and its relations to other areas of mathematics
Recommended from our members
Representations of Finite Groups
Get PDFThe workshop Representations of Finite Groups was organised by Joseph Chuang (London), Meinolf Geck (Stuttgart), Markus Linckelmann (London), and Gabriel Navarro (Valencia). It covered a wide variety of aspects of the representation theory of finite groups and related objects, such as algebraic groups
Recommended from our members
Representations of Finite Groups
Get PDFThe workshop "Representations of Finite Groups" was organised by Olivier Dudas (Marseille), Meinolf Geck (Stuttgart), Radha Kessar (Manchester), and Gabriel Navarro (Valencia). It covered a wide variety of aspects of the representation theory of finite groups and related topics, and showcased several recent breakthrough results
The decomposition numbers of the Hecke algebra of type 𝐸*₆
No full textLet
E
6
(
q
)
{E_6}(q)
be the Chevalley group of type
E
6
{E_6}
, over a finite field with q elements, l be a prime not dividing q, and
H
R
(
q
)
{H_R}(q)
be the endomorphism ring of the permutation representation (over a valuation ring R with residue class field of characteristic l) of
E
6
(
q
)
{E_6}(q)
on the cosets of a standard Borel subgroup
B
(
q
)
B(q)
. Then the l-modular decomposition matrix
D
l
{D_l}
of the algebra
H
R
(
q
)
{H_R}(q)
is a submatrix of the l-modular decomposition matrix of the finite group
E
6
(
q
)
{E_6}(q)
. In this paper we determine the matrices
D
l
{D_l}
, for all l, q as above. For this purpose, we consider the generic Hecke algebra H associated with the finite Weyl group of type
E
6
{E_6}
over the ring
A
=
Z
[
v
,
v
−
1
]
A = \mathbb {Z}[v,{v^{ - 1}}]
of Laurent polynomials in an indeterminate v, and calculate the decomposition matrices of H which are associated with specializations of v to roots of unity over
Q
\mathbb {Q}
or values in a finite field. The computations were done by using the computer algebra systems MAPLE and GAP.</p
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