PSL(2,19) Modulo 19
The Hecke algebra for the Projective Special Linear Group of dimension 2
over GF(19) with point stabilizer being the normalizer of a
Sylow 19-subgroup
in characteristic 19
.
The Module M
The module M is the permutation module over the prime
field of chacteristic 19, having point stablilizer
of order 171
The dimension of M is 20
.
The dimensions of the irreducible submodules modules are
19,
1
.
The module M has radical filtration (Loewy series)
1,
2
The module M has socle filtration (socle series)
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 dimensions of the projective modules are
19,
1
.
The cartan matrix of A is
The determinant of the Cartan matrix is 1.
The blocks of A consist of the following irreducible
modules: