On Monday, August 20, 2012 11:21:04 AM UTC-7, bsmile wrote:
>
>
>
> On Monday, August 20, 2012 12:56:07 PM UTC-5, John H Palmieri wrote:
>>
>>
>>
>> I don't know much about this aspect of Sage, but you can also try this:
>>
>> sage: rep = SymmetricGroupRepresentation([3,1])
>>
>> Now rep is the representation of S_4 (since 4=3+1) corresponding to the
>> partition [3,1]. We can compute find the matrix associated to each element
>> of S_4:
>>
>> sage: rep([1,4,3,2])
>> [ 1 0 0]
>> [ 1 -1 1]
>> [ 0 0 1]
>> sage: REPS = [(x,rep(x)) for x in S4.list()]
>>
>> This defines REPS to be a list of pairs, (elt of S_4, corresponding
>> matrix).
>>
>> Is that the sort of thing you want?
>>
>
> Thanks for your response. It's close, but not quite. It seems the way you
> pointed out does give a 3D irreducible matrix representation for S4. But
> how can I get the 2D irreducible matrix representation for S4?
>
Use a different partition. Every partition of 4 will give an irreducible
representation. You can get each of the representations like this:
sage: [SymmetricGroupRepresentation(p) for p in Partitions(4).list()]
--
John
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