PSL(2,16) Modulo 17
The Hecke algebra for the Projective Special Linear Group of dimension 2
over GF(16) with point stabilizer being the normalizer of a
Sylow 17-subgroup
in characteristic 17
.
The Module M
The module M is the permutation module over the
field of chacteristic 17, having point stablilizer
of order 34
. The dimension of M is 120
.
The dimensions of the irreducible submodules are
68,
34,
17,
1
.
The module is semi-simple. It has composition factors consisting of the
modules 1, 2, 3, 4.
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
17,
17,
17,
1
over field extensions of the prime field of degrees
4,
2,
1,
1
.