About SymmetricGroupRepresentation()
I am a new student in SAGE. I read the following discussion:
evaluation of character of symmetric group
and then also read the manual.
However, I am still confused about some fundamental problem:
(I cannot find these function in "Sage Reference Manual: Groups, Release 8.2". Are both new functions?).
About
SymmetricGroupRepresentation(partition, implementation='specht', ring=None, cache_matrices=True)
I am confused about "partition". Suppose for S3, and partition =[2,1]. What does it mean? (It seems [1,2] is not valid)
About
spc = SymmetricGroupRepresentation([2,1], 'specht') spc.representation_matrix(Permutation([1,2,3]))
When I use
spc.representation_matrix(Permutation([1,2]))
error pops out. However, as far as I know, (1,2) is a valid permutation, which represent the matrix representation: [010100001]
However, if I use 'orthogonal' instead of 'specht', the answer becomes
[1001]
But I test another permutation: [1,2,3], the answer is the same. However, [1,2] and [1,2,3] are in the different conjugacy classes; they should not have the same character.
I cannot find "Permutation" in "Sage Reference Manual: Group". Where can I find this function?