7 ,
1
The Hecke algebra for the Symmetric Group
on 8 Letters, with the Partition
[ 7, 1 ]
in characteristic 3
.
The Module M
The module M is the permutation module over the prime
field of chacteristic 3, having point stablilizer
equal to the Young subgroup of the partition.
The dimension of M is 8
.
The dimensions of the irreducible submodules modules are
7,
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
7,
1
.
The cartan matrix of A is
The determinant of the Cartan matrix is 1.
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