PSU(3,5) Modulo 5
The Hecke algebra for the Projective Special Unitary Group of dimension 3
over GF(5) with point stabilizer being the normalizer of a
Sylow 5-subgroup
in characteristic 5
.
The Module M
The module M is the permutation module over the
field of chacteristic 5, having point stablilizer
of order 1000
. The dimension of M is 126
.
The dimensions of the irreducible submodules modules are
125,
1
.
The module M is semi-simple. It has composition factors
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
125,
1
over field extensions of the base field of degrees
1,
1
.