PSL(2,32) Modulo 11
The Hecke algebra for the Projective Special Linear Group of dimension 2
over GF(32) with point stabilizer being the normalizer of a
Sylow 11-subgroup
in characteristic 11
.
The Module M
The module M is the permutation module over the
field of chacteristic 11, having point stablilizer
of order 66
. The dimension of M is 496
.
The dimensions of the irreducible submodules modules are
495,
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
33,
1
over field extensions of the base field of degrees
15,
1
.