8 ,
1
The Hecke algebra for the Symmetric Group
on 9 Letters, with the Partition
[ 8, 1 ]
in characteristic 2
.
The Module M
The module M is the permutation module over the prime
field of chacteristic 2, having point stablilizer
equal to the Young subgroup of the partition.
The dimension of M is 9
.
The dimensions of the irreducible submodules modules are
8,
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
8,
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:
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