Sz(8) Modulo 2
The Hecke algebra for the Suzuki Group over GF(8) with point stabilizer
being the normalizer of a
Sylow 2-subgroup
in characteristic 2
.
The Module M
The module M is the permutation module over the
field of chacteristic 2, having point stablilizer
of order 448
. The dimension of M is 65
.
The dimensions of the irreducible submodules modules are
64,
1
.
The module M is semi-simple. It has composition factors
consisting of modules
1,
2
The Action Algebra
The action algebra A is the image of kG in the
k-endomorphism ring of M. It's simple modules are the irreducible
submodules of M.
The algebra A is a direct product of matrix algebras
of dimension
64,
1
over field extensions of the base field of degrees
1,
1
.